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Articles and videos
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Geometry
- Géométriser l’espace : de Gauss à Perelman — le théorème d’uniformisation a cent ans ! by (November 17th, 2007) ► A simplified story of ’s Uniformization Theorem and ’s proof of Thurston’s Geometrisation Conjecture.
- Tinkertoy Models Produce New Geometric Insights — Geometric objects take on different properties depending on the space in which you visualize them. Using techniques from an upstart field called tropical geometry — which analyzes complicated shapes using sticklike models — mathematicians have gained a new sense of how those properties behave. by (September 5th, 2018) ► Tropical geometry creates a link between shapes and chip-firing game.
- What does this prove? Some of the most gorgeous visual "shrink" proofs ever invented by (July 25th, 2020) ► Using shrinking and contradiction to list the regular possible polygons in an integer lattice and the angles that have a rational sine / cosine / tangent.
- Qu'est-ce qu'un tenseur ? by (February 15th, 2023) ► The title says it all.
- Why are the formulas for the sphere so weird? (major upgrade of Archimedes' greatest discoveries) by (November 25th, 2023) ► Yet another ways to compute the area and the volume of a circle and of a sphere.
- Infinite Circles - Numberphile by (December 19th, 2023) ► It is impossible to partition a plane with circles, but it is possible to partition space.
- Number of Distances Separating Points Has a New Bound — Mathematicians have struggled to prove Falconer’s conjecture, a simple but far-reaching hypothesis about the distances between points. They’re finally getting close. by (April 9th, 2024) ► The subtitle says it all.
- Florestan Martin Baillon - La droite de Berkovich en images by (April 15th, 2024) ► A presentation of the Berkovich line.
- Five puzzles for thinking outside the box by (November 8th, 2024) ► Some puzzles that are much easier to solve by analyzing them in a higher dimension.
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2D
- The Most Mathematical Flag - Numberphile by (August 3rd, 2012) ► The Nepal flag is defined mathematically.
- Happy Ending Problem - Numberphile by (July 1st, 2014) ► The "happy ending problem" and Erdős–Szekeres conjecture.
- The Three Square Geometry Problem - Numberphile by (September 18th, 2014) ► A simple triangle problem.
- Euclid's Big Problem - Numberphile by (December 12th, 2014) ► What can be constructed with a ruler and a compass?
- ↪How to Trisect an Angle with Origami - Numberphile (December 12th, 2014) ► The title says it all.
- Math in the Simpsons: Homer's theorem by (September 4th, 2015) ► "The sum of the square root of any two sides of an isosceles triangle is equal to the square root of the remaining side." is wrong.
- Math is Illuminati confirmed by (September 19th, 2015) ► Morley’s Miracle, Napoleon’s theorem, and why the Winter Triangle appears as equilateral.
- ↪Math is Illuminati confirmed (PART 2): Morley's Miracle by (September 19th, 2015) ► ’s proof of Morley’s Miracle.
- Triangles have a Magic Highway - Numberphile by (February 1st, 2016) ► The orthocentre, the circumcentre, the centroid are on Euler line.
- ↪Triangle Centres and the Euler Line (extra footage) by (February 2nd, 2016) ► The continuation of the previous video, with the proof of some characteristics of these three points.
- Evil Geometry Problem by (February 28th, 2016) ► An impossible triangle.
- Rozenn Texier-Picard - Le problème isopérimétrique by (May 29th, 2016) ► A high-level description of ’s proof of the isoperimetric problem.
- How to Rotate any Curve by any Angle↓🚫 by (June 24th, 2016) ► The subject is interesting, but the computations are very painful.
- Deux (deux ?) minutes pour... le théorème de Bézout by (July 4th, 2016) ► Completing Bézout’s theorem to get a correct version: points at infinity, complex solutions, considering the multiplicity of intersection points, and excluding the case where the two curves have a common component.
- Le flexaèdre - Micmaths by (July 17th, 2016) ► How to build a HyperQBS.
- Too Many Triangles - Numberphile by (November 28th, 2016) ► Trying to layout seven triangles with a common vertex.
- The Moving Sofa Problem - Numberphile by (March 23rd, 2017) ► The initial problem and its ambidextrous version.
- Gauss's magic shoelace area formula and its calculus companion by (June 10th, 2017) ► The title says it all.
- Area of dodecagon | Beautiful geometry | Visual mathematics by (August 23rd, 2017) ► The title says it all.
- Four squares with constant area | Visual Proof | Squaring the segments | by (December 27th, 2017) ► An unclear visual proof.
- Cannons and Sparrows - Numberphile by (January 22nd, 2018) ► Trying to prove that a polygon can be split into n polygons of equal area and equal perimeter, by using heavy machinery.
- ↪Cannons and Sparrows (extra footage) - Numberphile by (May 20th, 2018) ► The continuation of the previous video.
- Round Peg in a Square Hole - Numberphile by (March 5th, 2018) ► A clever trick to get a disc through a smaller square.
- De l'ordre dans les tiroirs - Automaths #01🚫 by (March 11th, 2018) ► From the pigeonhole principle to Ramsey’s theorem and the Happy Ending Problem.
- Autour de la Terre - Automaths #03🚫 by (May 6th, 2018) ► The usual "string girdling Earth" puzzle.
- The Cross Ratio - Numberphile by (July 6th, 2018) ► Using the cross-ratio to compute a distance using a photo.
- Earthquakes, Circles and Spheres - Numberphile by (July 24th, 2018) ► Proving a 2D theorem by doing 3D geometry and a long digression about earthquakes.
- ↪Balls and Cones - Numberphile by (July 24th, 2018) ► The continuation of the previous video: another 2D theorem proven using 3D.
- Floating Bodies - Numberphile by (September 11th, 2018) ► The definitions of the floating body and the convex floating body with some 2D examples.
- ↪Continuation of Floating Bodies - Numberphile by (September 11th, 2018) ► The continuation of the previous video: some facts about convex floating bodies.
- Making a physical Lissajous curve by (September 14th, 2018) ► The title says it all.
- Secrets of the NOTHING GRINDER by (December 7th, 2018) ► The geometry of the trammel of Archimedes and Tusi couple.
- The secret of the 7th row - visually explained by (January 26th, 2019) ► Proving some properties of circles stacked between two walls.
- Réformons les angles ! - Micmaths by (January 27th, 2019) ► Another way to measure angles and some of its advantages.
- How many ways can circles overlap? - Numberphile by (April 14th, 2019) ► Counting the number of possibilities of intersecting/including n circles.
- Computing With Art - Computerphile↓ by (June 7th, 2019) ► A rather messy description of some physical systems generating Voronoi Diagrams.
- On mesure la tour Eiffel ! (avec Manu Houdart) by and (June 15th, 2019) ► Evaluating the height of Eiffel tower with a Jacob’s staff.
- Calculating the value of Pi by (June 26th, 2019) ► Some very basic geometry: using regular polygons to numerically evaluate π.
- 2000 years unsolved: Why is doubling cubes and squaring circles impossible? by (June 29th, 2019) ► Giving an idea of the proofs that it is impossible to double cubes, trisect angles, construct regular heptagons, and square circles.
- Voitures, PDF et courbes de Bézier - Automaths #14🚫 by (August 12th, 2019) ► A presentation of Bézier curves.
- Constructing a Square of Equal Area to a given Polygon by (August 19th, 2019) ► The title says it all.
- Deux (deux?) minutes pour la quadrature du cercle by (September 16th, 2019) ► A high-level description of how doubling the cube, trisecting an angle and squaring the circle have been proved impossible.
- Solve For The Radius by (November 29th, 2019) ► A little geometry problem.
- A fun probability puzzle with a neat geometric solution. by (December 6th, 2019) ► A simple geometry puzzle.
- How Simple Math Can Cover Even the Most Complex Holes — No one knows how to find the smallest shape that can cover all other shapes of a certain width. But high school geometry is getting us closer to an answer. by (January 8th, 2020) ► The title says it all.
- The Fermat Point of a Triangle | Geometric construction + Proof | by (February 9th, 2020) ► The definition of Fermat point and how to construct it.
- Mesolabe Compass and Square Roots - Numberphile by (March 15th, 2020) ► Using geometry to multiply two numbers or to compute a square root.
- 3 Ways to Draw Squares Inside Triangles - Numberphile by (March 22nd, 2020) ► Three solutions to the problem of inscribing a square in a triangle.
- 11 Geometry Puzzles That Drive Mathematicians to Madness by (April 15th, 2020) ► The real puzzle with is: how does she create such beautifully crafted puzzles?
- ★★★ Les Coordonnées Homogènes du Plan Projectif - La Saga des Espaces #3 by and (May 7th, 2020) ► The title says it all.
- Every Polygon can be Triangulated Into Exactly n-2 Triangles | Proof by Induction by (May 13th, 2020) ► The title says it all.
- Three unsolved problems in geometry by (June 16th, 2020) ► The Happy Ending problem, the Perfect Cuboid, and Toeplitz’ Conjecture.
- [AVENT MATHS] : 3 angles égaux🚫 by (December 3rd, 2020) ► Trisecting an angle with origami.
- [AVENT MATHS] : 22 parts de gâteau🚫 by (December 22nd, 2020) ► The lazy caterer’s sequence.
- ★ Apprendre la Géométrie Analytique avec les Droites - La Saga des Courbes Algébriques #1 by and (February 12th, 2021) ► An introduction to analytic geometry with the equations of lines and the case of projective geometry.
- Thomaths 12a : La Perspective I by (February 23rd, 2021) ► An introduction to perspective.
- ↪Thomaths 12b : La Perspective II, Géométrie projective (introduction) by (May 14th, 2021) ► Projective geometry: projective transformations, cross-ratio, poles, and conics.
- ↪Thomaths 12c : La Perspective III, Espace projectif by (August 13th, 2021) ► A presentation of projective spaces.
- Construire l'heptadécagone régulier (17 côtés) - Maths sans un mot #01 by (July 11th, 2021) ► The title says it all.
- Why the longest English word is PAPAL and SPA is the pointiest. by (August 18th, 2021) ► Useless geometrical calculation about the locations of the keys used to type a given word.
- What is the area of a Squircle? by (September 1st, 2021) ► From the squircle, to the lemniscate, to the arithmetic–geometric mean.
- The Strange Orbit of Earth's Second Moon (plus The Planets) - Numberphile by (September 14th, 2021) ► The trajectories of planets and of Cruithne in a geocentric frame.
- Les bretelles d'autoroutes ne sont pas des arcs de cercle ! by (September 15th, 2021) ► Euler spiral (a.k.a. clothoid).
- Measure the Earth’s Radius! (with this one complicated trick) by and (October 7th, 2021) ► A (total) failure to try to estimate Earth size (due to an incorrect measurement).
- Is there an equation for a triangle? by (December 1st, 2021) ► Creating a (not very nice) equation for a triangle.
- ↪Behold all-new equations for triangles! by (April 26th, 2023) ► Some equations proposed by viewers.
- The 3-4-7 miracle. Why is this one not super famous? by (December 30th, 2021) ► The analysis of a popular animation.
- Tunnelling through a Mountain - Numberphile by (January 23rd, 2022) ► The geometry used by Eupalinos to build a tunnel on Samos Island.
- An Ancient Geometry Problem Falls to New Mathematical Techniques — Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.↓ by (February 8th, 2022) ► There is very little information here.
- ↪Equi-décomposition et mesure (Quadrature du cercle de Tarski avec démo) - Passe-science #46 by (April 9th, 2022) ► An explanation of and demonstration.
- Drawing an Egg (with a Pentagon) - Numberphile by (April 16th, 2022) ► The title says it all.
- Heron’s formula: What is the hidden meaning of 1 + 2 + 3 = 1 x 2 x 3 ? by (May 14th, 2022) ► Proofs of Heron’s formula and Brahmagupta’s formula.
- Pythagoras twisted squares: Why did they not teach you any of this in school? by (October 15th, 2022) ► Some mathematical results related to the twisted squares diagram.
- Mathematicians Discover the Fibonacci Numbers Hiding in Strange Spaces — Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio. by (October 17th, 2022) ► Some results have been found for symplectic embeddings of ellipsoids, but, as many times with Quanta Magazine articles about specific mathematical domains, there is little information.
- Cow-culus and Elegant Geometry - Numberphile by (November 14th, 2022) ► Heron’s shortest path problem.
- ↪Cow-culus v Geometry (extra) - Numberphile by (November 15th, 2022) ► Two other similar problems.
- Can the Same Net Fold into Two Shapes?↑ by (December 3rd, 2022) ► Finding nets that can be folded into different rectangular cuboids, sometimes using clever tricks.
- Comment ranger des chocolats dans une boîte (mathématiquement) ? - Micmaths↑ by (December 18th, 2022) ► The problem of square packing in a square: what is known and the unresolved cases.
- Triangle Subdivision - Numberphile by (February 9th, 2023) ► Barycentric subdivision and edgewise subdivision.
- Mathematicians Complete Quest to Build ‘Spherical Cubes’ — Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes. by (February 10th, 2023) ► Some information about the link between the Unique Games Conjecture and "Spherical Cubes", but there are not enough details to understand the matter.
- La conjecture de Birch & Swinnerton-Dyer - Deux (deux ?) minutes pour...⇈ by (March 7th, 2023) ► A very good attempt at explaining the conjecture.
- The Perfect Goal Kicking Angle - Numberphile by (March 16th, 2023) ► An optimisation problem but there is no proof of optimality.
- Adrien Abgrall - Origami et nombres algébriques by (April 4th, 2023) ► Any algebraic number is constructible by origami if we allow ourselves to make multiple folds.
- QUE PERMETTENT DE CONSTRUIRE LES OUTILS GÉOMÉTRIQUES ? by (June 12th, 2023) ► A classic description of the discovery of the rules of constructibility with straightedge and compass.
- Mathematicians Solve Long-Standing Coloring Problem — A new result shows how much of the plane can be colored by points that are never exactly one unit apart. by (July 19th, 2023) ► The subtitle says it all.
- A needlessly complicated but awesome bridge. by (August 31st, 2023) ► How has been calculated the shape of Cody Dock Rolling Bridge so this it can be manually rolled.
- The Biggest Smallest Triangle Just Got Smaller — A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square. by (September 8th, 2023) ► The lower bound of Heilbronn triangle problem has been improved.
- The SAT Question Everyone Got Wrong by (November 30th, 2023) ► The Coin Rotation Paradox.
- Simple yet 5000 years missed ? by (February 24th, 2024) ► A property of triangles which has been discovered only in 2014.
- Conway's IRIS and the windscreen wiper theorem by (April 6th, 2024) ► The Conway’s Circle Theorem and the Side Divider Theorem.
- PETR'S MIRACLE: Why was it lost for 100 years? (Mathologer Masterclass)↑ by (June 8th, 2024) ► A presentation of Petr-Douglas-Neumann theorem.
- The Lazy Way to Cut Pizza - Numberphile by (August 12th, 2024) ► This is yet another presentation of the classical computation of the number of regions defined by n lines.
- Ptolemy’s Theorem and the Almagest: we just found the best visual proof in 2000 years by (September 7th, 2024) ► A "proof" of Ptolemy’s Theorem and some results derived from it.
- Le puzzle de Dudeney est optimal ! by (December 17th, 2024) ► "Dudeney’s Dissection is Optimal" proves that an equilateral triangle cannot be cut into three pieces that can be rearranged into a square.
- The Teleprompter Paradox by (February 28th, 2025) ► Some basic geometry to find the best distance between a speaker and the teleprompter.
- Cardioids in Coffee Cups - Numberphile by (April 20th, 2025) ► Circle caustics: nephroid and cardioid.
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Inversion
- Epic Circles - Numberphile by (April 13th, 2014) ► Using circle inversion to compute the radius of the circles of a Pappus chain.
- A Miraculous Proof (Ptolemy's Theorem) - Numberphile by (February 9th, 2020) ► A simple proof of Ptolemy’s theorem using inversion. The explanation is quite slow.
- ↪Pentagons and the Golden Ratio - Numberphile by (February 9th, 2020) ► The continuation of the previous video: two corollaries of Ptolemy’s theorem.
- ↪Inversion (extra) - Numberphile by (February 10th, 2020) ► The continuation of the previous video: some little more about inversion.
- Infinitely Many Touching Circles - Numberphile by (November 17th, 2021) ► Using circle inversion to draw a beautiful image.
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Euclid’s fifth axiom
- Les Ernest | Etienne Ghys : Et si le théorème de Pythagore n'était pas vrai ? by (2014) ► A short telling of the discovery of non-Euclidean geometries and the suggestion to teach them to children.
- Undecidability Tangent (History of Undecidability Part 1) - Computerphile by (September 19th, 2014) ► The story of the fifth axiom, but this is not a very good telling of this story.
- Ditching the Fifth Axiom - Numberphile by (April 10th, 2015) ► The description of Euclid’s postulates and the creation of hyperbolic geometry by negating the fifth one.
- ↪Fifth Axiom (extra footage) - Numberphile by (April 11th, 2015) ► The continuation of the previous video.
- Pi Day et géométrieS - Histoires de maths #01🚫 by (March 14th, 2019) ► Yet the same story.
- A Problem with the Parallel Postulate - Numberphile by (December 15th, 2022) ► A very classical presentation of the fifth axiom and non-Euclidean geometries.
- Les géométries non-euclidiennes (⧉) by (June 3rd, 2023) ► The same.
- How One Line in the Oldest Math Text Hinted at Hidden Universes by and (October 21st, 2023) ► Yer another presentation of the fifth axiom.
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Constructible polygons
- Deux (deux ?) minutes pour l'heptagone régulier by (October 24th, 2014) ► A short presentation of Gauss-Wantzel theorem and how to build the first regular polygons.
- [AVENT MATHS] : 17 côtés égaux🚫 by (December 17th, 2020) ► What are the constructible regular polygons?
- An Odd Property of the Sierpiński Triangle - Numberphile by (October 20th, 2024) ► The numbers of sides of odd contructible polygons generates the beginnng of Sierpiński triangle.
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The Pythagorean theorem
- A Mathematical Fable - Numberphile by (May 6th, 2014) ► A proof of the Pythagorean theorem.
- Deux minutes pour... le théorème de Pythagore by (September 24th, 2014) ► A speed run of proofs.
- Visualising Pythagoras: ultimate proofs and crazy contortions by (February 25th, 2018) ► A few proofs of the Pythagorean theorem and some other equations.
- Pythagorean theorem | 3 Visual Proofs | by (July 11th, 2018) ► The title says it all.
- The kissing circles theorem - challenging problem from Indonesia! by (October 5th, 2018) ► A simple problem of geometry.
- A Pythagorean Theorem for Pentagons + Einstein's Proof by (April 2nd, 2019) ► A slow description of the Pythagorean theorem.
- What Is The Length Of The Side? by (July 8th, 2019) ► A simple puzzle.
- Area of the Q - Numberphile by (September 9th, 2021) ► Computing the area of lunes.
- The British Flag Theorem by (May 24th, 2022) ► A simple description of the theorem.
- ↪Follow-up: British Flag Theorem by (June 1st, 2022) ► Some variations around the British flag theorem.
- ★★ Le Théorème de Pythagore : analyse de cas - Hors-Série by and (December 7th, 2022) ► The Pythagorean theorem creates a bridge between numbers and geometry, so, now that maths are based on numbers, it is more an axiom than a theorem.
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Pick’s theorem
- Proving Pick's Theorem | Infinite Series by (March 16th, 2017) ► The title says it all.
- Le théorème de Pick, avec Roger Mansuy - Myriogon #26 by and (May 4th, 2020) ► The high-level presentation of two proofs of the theorem.
- Pick's theorem: The wrong, amazing proof by (August 23rd, 2021) ► The title says it all.
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Viviani’s theorem
- Geometry: Viviani's theorem | Visualization + Proof | by (December 13th, 2017) ► The title says it all.
- Le théorème de Viviani - Automaths #16🚫 by (May 26th, 2020) ► A proof of the theorem and some applications.
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Conic sections
- Les coniques à la plage - Micmaths by (August 5th, 2015) ► Creating conic sections with sand.
- Multiplying monkeys and parabolic primes by (August 8th, 2015) ► Using a parabola to perform multiplication.
- Why slicing a cone gives an ellipse (beautiful proof) by (August 1st, 2018) ► A proof that the intersection of a cone and a plane is an ellipse.
- Une ellipse surgit - Automaths #12🚫 by (February 19th, 2019) ► Drawing an ellipsis by folding a paper disk.
- The Secret of Parabolic Ghosts by (March 16th, 2019) ► Some properties of parabolas.
- Generating Conic Sections with Circles | Part 1. The Ellipse by (August 29th, 2020) ► The title says it all.
- Why is there no equation for the perimeter of an ellipse‽ by (September 5th, 2020) ► Some formulas to evaluate the perimeter of an ellipsis.
- Poncelet's Porism - Numberphile by (September 19th, 2020) ► A description of Poncelet’s closure theorem with very little information.
- Thomaths 11 : Les Coniques by (November 8th, 2020) ► Five different ways to define the conic sections.
- Parabolas and Archimedes - Numberphile↓ by (May 23rd, 2021) ► A detailed description of the geometric construction Archimedes used to compute the area of a parabola, but the proof is not given. The only interesting point is that Archimedes invented calculus 2000 years before Newton and Leibniz.
- Conic Loaf of Bread - Numberphile by (December 25th, 2021) ► The usual description of conics as the intersection of a cone and a plane.
- The Journey to 3264 - Numberphile by (April 2nd, 2023) ► ’s problem: what is the number of conics tangent to five given conics?
- Parabolic Mirrors - Numberphile by (May 26th, 2023) ► Proving, by computation, that a parabola focuses rays to its focal point.
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Elliptic curves
- Without a Proof, Mathematicians Wonder How Much Evidence Is Enough — A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof? by (October 31st, 2018) ► A heuristic may change the common belief that the rank of elliptic curves is unbounded, but it is not a proof.
- How to Find Rational Points Like Your Job Depends on It — Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others. by (July 22nd, 2021) ► The subtitle says it all.
- Elliptic Curve ‘Murmurations’ Found With AI Take Flight — Mathematicians are working to fully explain unusual behaviors uncovered using artificial intelligence. by (March 5th, 2024) ► A phenomenon discovered while tinkering with machine learning is getting explained.
- New Elliptic Curve Breaks 18-Year-Old Record — Two mathematicians have renewed a debate about the fundamental nature of some of math’s most important equations. by (November 11th, 2024) ► An elliptic curve having a rank equal to 29 has been found.
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Reuleaux Triangles
- Shapes and Solids of Constant Width - Numberphile by (November 11th, 2013) ► Reuleaux Triangles and Meissner Tetrahedron.
- New Reuleaux Triangle Magic by (February 16th, 2019) ► Some properties of constant-width shapes.
- Lego Reuleaux Triangle Mechanisms レゴでルーローの三角形↑ by (July 25th, 2020) ► Some spectacular Lego mechanisms based on Reuleaux Triangle.
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Kakeya’s Needle Problem
- Kakeya's Needle Problem - Numberphile by (October 15th, 2015) ► The title says it all.
- The Kakeya needle problem (the squeegee approach) by (October 26th, 2015) ► A short description of Besicovitch construction.
- Trajectoires #14 : En cheminant avec Kakeya, Vincent Borrelli et Jean Luc Rullière by and (June 14th, 2018) ► The Kakeya needle problem, Kakeya conjecture, and the relation with prime numbers.
- L'aiguille de Kakeya, avec Vincent Borrelli - Myriogon #10 by and (March 31st, 2020) ► The same information.
- Samuel Etourneau - Sur le problème de Kakeya by (August 25th, 2020) ► A very short telling of the story.
- A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special — The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true. by (July 26th, 2022) ► The current progress on proving Kakeya conjecture, but there are no mathematical details.
- New Proof Threads the Needle on a Sticky Geometry Problem — A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures. by (July 11th, 2023) ► Yet another step toward proving Kakeya conjecture.
- A Tower of Conjectures That Rests Upon a Needle — On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics. by (September 12th, 2023) ► Three conjectures, each depending on the previous one: the Kakeya conjecture, the restriction conjecture, and the Bochner-Riesz conjecture.
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The area of a cycloid arch
- Area under an arch of a cycloid by (April 3rd, 2018) ► The video is nice as usual, but there is no proof or explanation here.
- What is the area under an arc of a cycloid curve? by (January 27th, 2019) ► The same with another way to perform the computation.
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Biggest little polygon
- The Largest Small Hexagon - Numberphile by (December 17th, 2021) ► The biggest little polygons: the ones of largest area while having a radius of 1.
- Le plus grand des petits hexagones - Micmaths by (October 30th, 2023) ► The same.
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Goat problems
- After Centuries, a Seemingly Simple Math Problem Gets an Exact Solution — Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now. by (December 9th, 2020) ► The goat problem in 2 and higher dimensions, and the closed form solution found by .
- How to Solve Equations That Are Stubborn as a Goat — Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century. by (May 6th, 2021) ► Grazing goat problems: from the simplest to ’s result.
- The Goat Problem - Numberphile by (December 24th, 2022) ► Still the same…
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Billiard problems
- The Illumination Problem - Numberphile by (February 28th, 2017) ► The title says it all.
- ↪Problems with Periodic Orbits - Numberphile by (March 1st, 2017) ► The continuation of the previous video: can a light ray have a closed path?
- Elise Goujard - La baguette magique d'Eskin-Mirzakhani by (December 18th, 2019) ► The Magic Wand Theorem of and of .
- Unfolding the Mysteries of Polygonal Billiards — The surprisingly subtle geometry of a familiar game shows how quickly math gets complicated. by (February 15th, 2024) ► A good overview of the current knowledge on billiard and illumination problems.
- Is pool actually just mathematics? by , , , and (June 21st, 2024) ► The physics of pool is more complicated than the usual mathematical model.
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Laser in a square mirror room
- The Assassin Puzzle | Infinite Series by (May 17th, 2018) ► The description of the puzzle and some tips to solve it.
- ↪Is the Square a Secure Polygon? by (May 17th, 2018) ► The counterintuitive solution of the previous puzzle.
- How to avoid being hit by a laser in a room of mirrors by (July 25th, 2021) ► A simulation.
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3D
- The Napkin Ring Problem by (August 14th, 2017) ► Simple geometry proves that the napkin volume is independent of the original sphere’s radius.
- All UK football road signs are wrong! Join the petition for geometric change! by (October 9th, 2017) ► launches a petition to correct a road sign which is mathematial nonsense.
- ↪The mathematically impossible ball that shouldn’t exist. by (May 22nd, 2024) ► The UK government parliament refused to modify road signs, so now proposes to modify the ball…
- Ham Sandwich Problem - Numberphile by (December 15th, 2017) ► The ham sandwich theorem.
- THE SCUTOID: did scientists discover a new shape? by , , and (August 3rd, 2018) ► A presentation of the scutoid, a shape of some epithelial cells.
- 5-Sided Square - Numberphile by (August 13th, 2018) ► A presentation of what is a pseudosphere and how to draw a pentagon with five right angles on it.
- The Best Way to Pack Spheres - Numberphile by (September 24th, 2018) ► The history of the proving the highest sphere density and how to compute it.
- Cavalieri's Principle in 3D | Volume of a sphere | by (October 2nd, 2018) ► Determining the volume of a sphere from the volume of a cone.
- A Strange Map Projection (Euler Spiral) - Numberphile by (November 13th, 2018) ► Peeling an orange along a spiral and flattening the strip gives a Euler spiral.
- But why is a sphere's surface area four times its shadow? by (December 2nd, 2018) ► The title says it all: two proofs of the relationship.
- The Dehn Invariant - Numberphile↑ by (July 14th, 2019) ► The proof that a polygon can be cut and rearranged into any polygon of the same surface and the proof that this cannot be done with polyhedra of the same volume.
- Curvahedra: how many faces make a polyhedron by and (July 20th, 2019) ► Curvahedra and the Gauss–Bonnet theorem.
- The Girl with the Hyperbolic Helicoid Tattoo - Numberphile by (September 29th, 2019) ► An explanation of hyperbolic helicoids.
- Spherical Geometry: Deriving The Formula For The Area Of A Spherical Triangle by (March 21st, 2020) ► Girard’s Theorem: £[area(T)=r^2(α+β+γ−π)£].
- Thomaths 6 : La forme de l'Univers ? by (May 4th, 2020) ► Some miscellaneous ideas: topology, curvature, random surfaces.
- there are 48 regular polyhedra by (August 2nd, 2020) ► The title says it all.
- [AVENT MATHS] : 8 deltaèdres convexes🚫 by (December 8th, 2020) ► A presentation of the eight convex deltahedra.
- Butterflies and Gyroids - Numberphile by (December 17th, 2020) ► Diffraction on butterfly wings.
- I wired my tree with 500 LED lights and calculated their 3D coordinates. by (December 24th, 2020) ► Determining the 3D coordinates of the LEDs and, then, creating lightning effects with them.
- ↪I run untested, viewer-submitted code on my 500-LED christmas tree. by (January 12th, 2021) ► The title says it all.
- ↪My 500-LED xmas tree got into Harvard. by (December 25th, 2021) ► redoes is once again, this time he detects the wrongly placed LEDs resulting from his simplistic localisation algorithm.
- The Volume of a Sphere - Numberphile by (June 20th, 2021) ► How Archimedes could have determined the volume of a sphere.
- Why (I thought) the Euro Ball being a Rhombicuboctahedron (would be) good for England. by (July 10th, 2021) ► The geometry of a ball.
- Why Do Bees Make Rhombic Dodecahedrons? by and (October 6th, 2021) ► The geometry of honeycombs.
- The bubble that breaks maths. by (November 5th, 2021) ► The minimal surface passing through two circles.
- Thomaths 14 : Les plus beaux solides de l'espace by (November 18th, 2021) ► Platonic solids, Archimedean solids, Johnson solids, Kepler–Poinsot polyhedra, and Goldberg polyhedra.
- Rémi Coulon - Le monde étrange de sol by (January 24th, 2022) ► A presentation of Sol geometry, a non-Euclidean geometry.
- The Tetrahedral Boat - Numberphile by (February 26th, 2022) ► About ’s sculptures based on tetrahedra.
- Father-Son Team Solves Geometry Problem With Infinite Folds — The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension. by (April 4th, 2022) ► Any polyhedron can be flatten by using an infinite number of creases.
- Making efficient Platonic and Archimedean shapes in a kaleidoscope by (December 6th, 2022) ► Generating regular solids with kaleidoscopes.
- Thomaths 21 : Des Nouvelles des Solides de Platon by (February 15th, 2023) ► Some recent discoveries related to Platonic solids.
- How many ways can you join regular pentagons? by (July 7th, 2023) ► The title of the paper ("A Complete List of All Convex Polyhedra Made by Gluing Regular Pentagons") which contains the real maths says it all.
- Mirror-image Mirror Balls: introducing the Kite-Rhombus Hectapentacontahedron by (August 21st, 2023) ► Yet another 3D solid, but this video contains little geometry.
- La conjecture de Kepler- Comment ranger ses boulets ? (⧉) by (October 10th, 2023) ► The story of Kepler’s conjecture and ’ proof.
- The Neat Alignment of the World's Biggest Antiprism by and (October 18th, 2023) ► Computing the volume of an "antifrustrum".
- Why does Vegas have its own value of pi? by and (October 24th, 2023) ► Some simple sphere geometry and analysing how an image displaying a truncated π value has been generated.
- ↪Vegas Sphere UPDATE: we fixed it! by and (October 27th, 2023) ► The π value has been fixed.
- Le secret de l'anamorphose - Micmaths by (November 7th, 2023) ► How to build an anamorphosis.
- What's the curse of the Schwarz lantern? by (December 23rd, 2023) ► A presentation of the Schwarz lantern: an approximation of a cylinder made of triangles whose total surface, as we increase the number of triangles, may diverge or converge to a value other than the cylinder surface.
- The Five Compound Platonic Solids by (March 6th, 2024) ► Playing with a dodecahedron and regular compound polyhedra.
- Cones are MESSED UP - Numberphile by (May 28th, 2024) ► The counterintuitive volume of cones.
- Où faut-il construire ces palais ? - Micmaths by (May 28th, 2024) ► How to position n points on a sphere so they are as distant one of each other as possible?
- New 7-direction pencil model discovered! by (May 31st, 2024) ► A lengthy way to arrange pencils.
- The shape that should be impossible. by (June 5th, 2024) ► How to build a polyhedron where all dihedral angles are right except for one.
- The search for the biggest shape in the universe. by (August 16th, 2024) ► found the polyhedron having its eight points on the unit sphere which has the largest volume using a Burroughs 220 computer.
- Xavier Saint-Raymond - Concours de hauteurs by (February 13th, 2025) ► A theorem on the intersections of the heights of a tetrahedron.
- Can I 3D print a minimal infinite surface? by (February 14th, 2025) ► is advertising for a 3D printer and arranges pencils in a gyroid.
- Golf balls: how many holes in one? by and (February 27th, 2025) ► Are golf balls Goldberg polyhedra?
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The Descartes-Euler polyhedral formula
- Euler's Formula V - E + F = 2 | Proof by (June 13th, 2020) ► A unusual proof of the formula (but it is not fully rigorous).
- [AVENT MATHS] : 2, Euler et les ballons de foot🚫 by (December 2nd, 2020) ► A presentation of the formula.
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Prince Rupert’s cube
- The cube shadow theorem (pt.1): Prince Rupert's paradox by (July 20th, 2017) ► ’s unit cube shadow theorem.
- ↪The cube shadow theorem (pt.2): The best hypercube shadows by (July 20th, 2017) ► The continuation of the previous video.
- Fitting a Cube Through a Copy of Itself | Rupert's Cube | by (December 3rd, 2017) ► A visualisation of the paradox.
- Can you make a hole in a thing bigger than the thing? by (October 31st, 2021) ► Prince Rupert’s paradox with pumpkins.
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Dice
- Fair Dice (Part 1) - Numberphile by (September 14th, 2016) ► Defining what is a fair dice and building the list of all of them.
- ↪Fair Dice (Part 2) - Numberphile by (September 15th, 2016) ► The continuation of the previous video.
- La forme des dés - Automaths #07↑🚫 by (August 29th, 2018) ► A lot of information about the geometry of dice.
- Le dé ultime - Micmaths by (April 5th, 2019) ► An explanation why the disdyakis triacontahedron is the best die.
- ↪J'ai oublié de lancer le dé ! - Micmaths by (April 9th, 2019) ► The continuation of the previous video.
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Geodesics on a dodecahedron
- A New Discovery about Dodecahedrons - Numberphile by (January 14th, 2020) ► There is a trajectory from a vertex to itself going through no other vertex on a dodecahedron.
- Mathematicians Report New Discovery About the Dodecahedron — Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid. by (August 31st, 2020) ► , and have classified the straight paths, starting and ending at a given corner and passing through no other corner, into 31 families.
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Higher dimensions
- Perfect Shapes in Higher Dimensions - Numberphile by (March 23rd, 2016) ► How many regular polytopes exist in dimensions other than 3?
- A Breakthrough in Higher Dimensional Spheres | Infinite Series | PBS Digital Studios by (November 17th, 2016) ► The weirdness of hyperspheres and ’s recent result (the best sphere packing in dimensions 8 and 24).
- Dissecting Hypercubes with Pascal's Triangle | Infinite Series by (June 1st, 2017) ► Determining the intersection of a hypercube by a hyperplane.
- 4D MONKEY DUST by (June 15th, 2017) ► An unclear description of a 4D stereographic projection.
- The Honeycombs of 4-Dimensional Bees ft. Joe Hanson | Infinite Series by (August 3rd, 2017) ► The honeycomb conjecture in 2D and Weaire–Phelan structure in 3D.
- Braids in Higher Dimensions - Numberphile by (August 24th, 2017) ► What kind of objects can be braided in 4 or higher dimensions?
- ↪Braids (extra footage) - Numberphile by (September 9th, 2017) ► The continuation of the previous video.
- Higher-Dimensional Tic-Tac-Toe | Infinite Series by (September 21st, 2017) ► For larger grids and higher dimensions, when is the first player sure to win?
- Statistics Postdoc Tames Decades-Old Geometry Problem — To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry. by (March 1st, 2021) ► A presentation of Bourgain’s Slicing Problem and Kannan, Lovász, and Simonovits Conjecture on which made recent big progress.
- How many 3D nets does a 4D hypercube have? by (May 14th, 2021) ► launches an initiative (WHUTS) to find the 3D unfoldings of a 4D hypercube that can tile space.
- The Iron Man hyperspace formula really works (hypercube visualising, Euler's n-D polyhedron formula) by (August 28th, 2021) ► The coefficients of £[(x+2)^n£] gives the numbers of vertices, edges, faces… of a n-dimensional cube.
- The Journey to Define Dimension — The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it. by (September 13th, 2021) ► A good classical presentation of the notion of dimension.
- Alicia Boole au pays des polytopes (⧉) by (October 10th, 2023) ► , Flatland, and the six regular polytopes.
- Mathematicians Discover New Shapes to Solve Decades-Old Geometry Problem — Mathematicians have long wondered how “shapes of constant width” behave in higher dimensions. A surprisingly simple construction has given them an answer. by (September 20th, 2024) ► Shapes of constant width that are exponentially smaller than the ball when the number of dimensions increases have been found.
- 2025, la quatrième dimension et les 1000$ de Conway - Micmaths by (January 13th, 2025) ► What are dioprims and the fact that 2025 is a tritriduoprismic number.
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The strangeness of high-dimensional spheres in cubes
- Thinking outside the 10-dimensional box by (August 12th, 2017) ► Trying to get a feeling of the phenomena by looking at the squares of the coordinates.
- Strange Spheres in Higher Dimensions - Numberphile by (September 18th, 2017) ► The usual description of the phenomena.
- ↪Strange Spheres (extra footage) - Numberphile by (September 20th, 2017) ► The continuation of the previous video.
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The Necklace splitting problem
- Using topology for discrete problems | The Borsuk-Ulam theorem and stolen necklaces by (November 18th, 2018) ► Using Borsuk-Ulam Theorem to prove a discrete necklace property.
- Necklace Splitting (a lesson for jewel thieves) - Numberphile by (June 18th, 2019) ► A non-technical description of the theorem by one of its authors.
- ↪Necklace Splitting (extra) - Numberphile by (August 10th, 2019) ► The continuation of the previous video.
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Kissing spheres
- Kissing Numbers - Numberphile by (October 10th, 2018) ► Kissing numbers are known for dimensions 1, 2, 3, 4, 8 and 24.
- Spheres and Code Words - Numberphile by (October 28th, 2018) ► The density of packed spheres for high dimensions.
- Out of a Magic Math Function, One Solution to Rule Them All — Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space. by (May 13th, 2019) ► proves that E8 and Leech lattices are the best arrangements for repelling forces.
- [AVENT MATHS] : 24 dimensions🚫 by (December 24th, 2020) ► A very quick presentation of Leech lattices and kissing numbers.
- Mathematicians Discover New Way for Spheres to ‘Kiss’ — A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches. by (January 15th, 2025) ► and made some progress on the lower bound of the kissing number in dimensions 18 to 21.
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Hyperbolic geometry
- Playing Sports in Hyperbolic Space - Numberphile by (May 18th, 2015) ► Some surprising characteristics of hyperbolic geometry.
- ↪More Hyperbolic Sports - Numberphile by (May 26th, 2015) ► The continuation of the previous video.
- Vincent Guirardel - Promenade hyperbolique by (December 12th, 2019) ► The paradox of the flanged steering wheel.
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Finite geometry
- Dobble et la géométrie finie by (May 4th, 2001) ► A mathematical analysis of Dobble.
- My adventures in 3D printing: Seven Triples puzzle by (November 7th, 2019) ► A game based on Fano plane.
- How does Dobble (Spot It) work? by (April 30th, 2021) ► An explanation on how Dobble and similar games have been created.
- ↪How I made a game with 10,303 different cards! by (April 30th, 2021) ► How tried, and failed, a larger Dobble.
- These 27 tickets guarantee a win on the Lottery by (July 30th, 2023) ► How to generate 27 tickets so at least one is a win in the UK National Lottery.
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Topology
- Topology of a Twisted Torus - Numberphile↓ by (January 27th, 2014) ► This is simply about cutting a torus into linked rings.
- Unexpected Shapes (Part 1) - Numberphile by (November 18th, 2015) ► The different results of cutting two attached Möbius strips.
- ↪Unexpected Shapes (Part 2) - Numberphile by (November 19th, 2015) ► The continuation of the previous video.
- ↪Cute Paper Trick - Numberphile by (November 21st, 2015) ► The continuation of the previous video.
- A Hole in a Hole in a Hole - Numberphile by (September 8th, 2016) ► From a hole in a hole in a hole to a three holes doughnut.
- ↪Extra on a Hole in a Hole in a Hole - Numberphile by (September 9th, 2016) ► The continuation of the previous video.
- Super Bottle - Numberphile by (December 13th, 2016) ► The classification of 2-manifolds (number of borders, single vs. double sided, and genus) and how to create a 2-manifold of a given genus.
- Hypertwist: 2-sided Möbius strips and mirror universes by (December 31st, 2016) ► The title says it all.
- Topology Riddles | Infinite Series by (May 11th, 2017) ► A good short introduction to topology.
- Deux (deux?) minutes pour... le théorème de Jordan by (June 23rd, 2017) ► Jordan curve theorem and the difficulty to prove something that seems obvious.
- Topology vs "a" Topology | Infinite Series by (December 21st, 2017) ► Getting a feeling of what is a topology.
- Proving Brouwer's Fixed Point Theorem | Infinite Series↓ by (January 18th, 2018) ► This proof is unclear, probably because the speaker goes much too fast on the details.
- Deux (deux?) minutes pour la conjecture de Poincaré↑ by (December 15th, 2018) ► A good try to explain topology and Poincaré conjecture.
- Tentacles Akimbo (with Cliff Stoll) - Numberphile by (February 16th, 2020) ► Deforming a double-doughnut into two linked rings with blown glass or with a human body.
- ↪Tentacles Akimbo (extra) - Numberphile by (March 8th, 2020) ► The continuation of the previous video.
- Thomaths 7b : Topologie algébrique (introduction) by (June 10th, 2020) ► Some invariants of algebraic topology: the connected components, the topological dimension, the Euler characteristic, and the fundamental group.
- 12 Curiosités Topologiques - Micmaths by (December 28th, 2020) ► The title says it all.
- How Mathematicians Use Homology to Make Sense of Topology — Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data. by (May 11th, 2021) ► The title says it all.
- Why does this balloon have -1 holes? by (July 30th, 2021) ► An introduction to topology and its strangeness.
- New Math Book Rescues Landmark Topology Proof — Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it. by (September 9th, 2021) ► The subtitle says it all.
- Solving the mystery of the impossible cord. by and (September 17th, 2021) ► Some information about knots and some humour.
- La conjecture de Poincaré (⧉) by (October 23rd, 2021) ► A presentation of topology and Poincaré conjecture.
- Lucien Grillet - La sphère cornue d’Alexander by (June 29th, 2022) ► The Jordan–Schoenflies theorem is invalid in 3D, the Alexander horned sphere is a counter-example.
- The Puzzling Fourth Dimension (and exotic shapes) - Numberphile by (December 1st, 2022) ► A basic presentation of exotic spheres and why topology is difficult in 4D.
- Mathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions — Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.↓ by (April 22nd, 2024) ► A typical Quanta Magazine’s mathematical article: there is so little maths that you have no real clue about what it speaks about.
- Thomaths 29 - Ruban de Möbius optimal by (February 21st, 2025) ► ¹s proof that the smallest Möbius strip has size £[\sqrt{3} \times 1£].
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Klein bottle
- A mirror paradox, Klein bottles and Rubik's cubes by (June 21st, 2015) ► Some little information about Möbius strip and Klein bottle.
- Hunt for the Elusive 4th Klein Bottle - Numberphile by (June 24th, 2015) ► The title says it all.
- ↪Can you REALLY put a Rubik's cube in a Klein bottle? by (August 1st, 2015) ► The continuation of the previous video, but there is no mathematics here, just playing with magnets.
- How to make a Klein Bottle from an old pair of jeans - Numberphile by (July 4th, 2018) ► Creating a Klein bottle with torn trousers.
- The 17-Klein Bottle - Numberphile by (February 23rd, 2020) ► A Möbius strip of Klein bottles.
- How to Fill a Klein Bottle - Numberphile by (March 1st, 2020) ► How to fill something which has no interior.
- The Coca-Cola Klein Bottle - Numberphile by (March 9th, 2022) ► is, as usual, excited to speak about his Klein bottles.
- Making a Glass Klein Bottle - Numberphile by and (November 24th, 2022) ► makes a glass Klein bottle.
- Your Klein Bottle is in the Post - Numberphile by (March 7th, 2023) ► explains his shipping process.
- The World's LONGEST Klein Bottle - Numberphile↓ by (April 11th, 2025) ► A stupid elongation of a Klein bottle.
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Sphere eversion (a.k.a. Smale’s paradox)
- Outside In (⧉) by , , , , , and (1994) ► Thurston’s eversion.
- Smale's inside out paradox by (November 5th, 2016) ► ’s eversion.
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∞ + 1
- Asteroids on a Donut by (February 18th, 2017) ► An introduction to manifolds.
- Manifold Menagerie by (February 28th, 2017) ► Klein bottle, two-holed torus, ℝℙ2.
- The Birth of Metrics by (March 4th, 2017) ► A basic explanation of the Riemannian Metric.
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The Rectangular Peg Problem
- Who cares about topology? (Old version) by (November 4th, 2016) ► Proving the inscribed rectangle theorem by using topology.
- New Geometric Perspective Cracks Old Problem About Rectangles — While locked down due to COVID-19, Joshua Greene and Andrew Lobb figured out how to prove a version of the “rectangular peg problem.” by (June 25th, 2020) ► A proof that a smooth closed curve contains four points forming a rectangle of any given ratio.
- This open problem taught me what topology is by (December 24th, 2024) ► A new version of the video on the Rectangular Peg Problem.
- ↪"Secret" Endscreen Vlog #4 by (January 9th, 2025) ► Some information about the making of the previous video.
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Knot theory
- What is a Knot? - Numberphile by (August 3rd, 2015) ► An introduction to mathematical knots.
- ↪Prime Knots - Numberphile by (August 10th, 2015) ► The continuation of the previous video.
- Borromean Ribbons - Numberphile by (May 19th, 2016) ► An example of Borromean rings.
- Unraveling DNA with Rational Tangles | Infinite Series by (March 29th, 2018) ► A short presentation of Rational Tangles.
- Neon Knots and Borromean Beer Rings - Numberphile by (April 9th, 2018) ► A basic presentation of the Borromean rings, but this is more about Cliff’s personal story.
- Graduate Student Solves Decades-Old Conway Knot Problem — It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway. by (May 19th, 2020) ► The Conway knot is not slice.
- Colouring Knots - Numberphile by (October 11th, 2020) ► An explanation of the tricolourability of knots.
- ↪Colouring Knots (extra) - Numberphile by (October 15th, 2020) ► The continuation of the previous video with more aspects of the knot theory: polynomials, links…
- Une énigme de 50 ans résolue : le nœud de Conway n'est pas bordant - Micmaths↑ by (October 17th, 2020) ► A short and very clear introduction to knot theory: colourability, Alexander polynomial, Jones polynomial, and slice knot.
- Untangling Why Knots Are Important — The study of knots binds together the interests of researchers in fields from molecular biology to theoretical physics. The mathematicians Colin Adams and Lisa Piccirillo discuss why with host Steven Strogatz. by , , and (April 6th, 2022) ► An introduction to knot theory and describes how she proved the Conway knot is not a slice knot.
- Mathematical Hugs (and Chiral Knots) - Numberphile by (June 21st, 2022) ► A basic presentation of knot chirality.
- ↪Mathematical Hugs and Knots (extra) by (July 1st, 2022) ► The continuation of the previous video.
- Mathematicians Eliminate Long-Standing Threat to Knot Conjecture — A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t. by (February 2nd, 2023) ► This description of the slice-ribbon conjecture and the fact that a possible counter-example is probably not one is difficult to understand.
- The Insane Math Of Knot Theory↑ by (September 3rd, 2023) ► The history of knot theory.
- Knot Surfaces - Numberphile by and (November 15th, 2024) ► The principles for generating a 3D surface from a knot are not clear for me.
- Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal — Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge. by (November 26th, 2024) ► The subtitle says it all.
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Toroflux
- Toroflux paradox: making things (dis)appear with math by (October 6th, 2018) ► A presentation of some ’s disappearance tricks, the missing square puzzle and torus knots.
- L'incroyable Toroflux ! by and (March 29th, 2025) ► Another presentation of Toroflux.
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Trigonometry
- Visual Calculus: Derivative of sin(θ) is cos(θ) by (April 9th, 2019) ► The title says it all.
- Don't combine the fractions, do this! by (April 29th, 2020) ► Using trigonometry formulas to prove that if £[\frac{a-b}{1+ab}+\frac{b-c}{1+bc}+\frac{c-a}{1+ca}=0£] then £[a=b£], £[b=c£], or £[c=a£].
- A Surprising Pi and 5 - Numberphile by (May 31st, 2020) ► The explanation of a simple trick with a calculator.
- Beautiful Trigonometry - Numberphile by (June 16th, 2020) ► Some animations to explain trigonometric functions.
- What is wrong with this sine memorisation pattern? by (June 20th, 2022) ► Why this memorisation trick is awful.
- Sum of arctan three ways by (December 28th, 2022) ► Three ways to compute £[arctan(1)+arctan(2)+arctan(3)=\pi£].
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Rational trigonometry:
This is bullshit.
Wildberger claims to have invented a new way to handle trigonometry, but this is just a rather simple rewrite of things known for a long time.
This may amuse a teenager interested by playing with mathematics.- An Invitation to Geometry | WildTrig: Intro to Rational Trigonometry 0 | N J Wildberger🚫 by (April 5th, 2008) ► The introduction of the series and some advertisement for his book. He explains that some reasoning can be wrong because based on what we see on a drawing. He does such reasoning in the following videos…
- ↪Why Trig is Hard | WildTrig: Intro to Rational Trigonometry | N J Wildberger🚫 by (November 6th, 2007) ► A reminder of the trigonometry as it is commonly taught.
- ↪Quadrance via Pythagoras and Archimedes | WildTrig: Intro to Rational Trigonometry | N J Wildberger🚫 by (November 8th, 2007) ► The presentation of quadrance, Pythagoras’ theorem, and triple quad formula.
- ↪Spread, Angles and Astronomy | WildTrig: Intro to Rational Trigonometry | N J Wildberger🚫 by (November 11th, 2007) ► The presentation of spread.
- ↪Five Main Laws of Rational Trigonometry | WildTrig: Intro to Rational Trigonometry | N J Wildberger🚫 by (November 12th, 2007) ► The demonstration of three new formulas: the spread law, the cross law, and the triple spread formula.