Euclidean solid geometry | Constant width | Geometric shapes
The Reuleaux tetrahedron is the intersection of four balls of radius s centered at the vertices of a regular tetrahedron with side length s. The spherical surface of the ball centered on each vertex passes through the other three vertices, which also form vertices of the Reuleaux tetrahedron. Thus the center of each ball is on the surfaces of the other three balls. The Reuleaux tetrahedron has the same face structure as a regular tetrahedron, but with curved faces: four vertices, and four curved faces, connected by six circular-arc edges. This shape is defined and named by analogy to the Reuleaux triangle, a two-dimensional curve of constant width; both shapes are named after Franz Reuleaux, a 19th-century German engineer who did pioneering work on ways that machines translate one type of motion into another. One can find repeated claims in the mathematical literature that the Reuleaux tetrahedron is analogously a surface of constant width, but it is not true: the two midpoints of opposite edge arcs are separated by a larger distance, (Wikipedia).
Billiard in a Reuleaux triangle
Seeing the billiard in a Reuleaux triangle was a wish by several viewers (including, I believe, Carmen, Bogdan, Auferen, Bluelightzero and Jonathan), so here it finally is! The Reuleaux triangle is a shape of constant width. You can build it by starting from an equilateral triangle, and t
From playlist Particles in billiards
Reuleaux Triangles - GCSE Higher extension
Proving the area and perimeter of a Reuleaux triangle. Mathologer video on shapes of constant width (really awesome!) - https://youtu.be/-eQaF6OmWKw
From playlist Geometry Revision
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2Uh3
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Why are manhole covers round? - Marc Chamberland
View full lesson: http://ed.ted.com/lessons/why-are-manhole-covers-round-marc-chamberland Why are most manhole covers round? Sure it makes them easy to roll, and slide into place in any alignment. But there’s another, more compelling reason, involving a peculiar geometric property of circ
From playlist New TED-Ed Originals
Shapes and Solids of Constant Width - Numberphile
Get them at Maths Gear: http://bit.ly/mathsgear More links & stuff in full description below ↓↓↓ Steve Mould discusses shapes and solids of constant width, including the Reuleaux triangle and the UK's 50p coin. Brown papers: http://bit.ly/brownpapers NUMBERPHILE Website: http://www.numb
From playlist Festival of Spoken Nerd on Numberphile
When do interacting organisms gravitate to the vertices of a regular simplex? - Robert McCann
Analysis Seminar Topic: When do interacting organisms gravitate to the vertices of a regular simplex? Speaker: Robert McCann Affiliation: University of Toronto Date: February 03, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
50 pence for your thoughts - Billiard in a 7-sided Reuleaux t̶r̶i̶a̶n̶g̶l̶e̶ polygon
Simulation of 20 000 particles reflected on the sides of a 7-sided Reuleaux t̶r̶i̶a̶n̶g̶l̶e̶ polygon (or Reuleaux heptagon). This shape is constructed from a regular heptagon by replacing each side by a circular arc centered on the opposite corner. It is a shape of constant width, that is
From playlist Particles in billiards
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.
From playlist 3D printing
Phase space representation of the billiard in Reuleaux-like heptagons
The billiard in this simulation is obtained by replacing the sides of a regular heptagon by circular arcs. The radius of the arcs varies between the 1 and 50, when measured in terms of the circumradius of the initial heptagon. A genuine "Reuleaux heptagon", similar to the Reuleaux triangle
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What are the properties that make up a rhombus
👉 Learn how to solve problems with rhombuses. A rhombus is a parallelogram such that all the sides are equal. Some of the properties of rhombuses are: all the sides are equal, each pair of opposite sides are parallel, each pair of opposite angles are equal, the diagonals bisect each other,
From playlist Properties of Rhombuses
NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today's video is about plane shapes that, just like circles, have the same width in all possible directi
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Cardboard Tetrahedron Pyramid Perfect Circle Solar How to make a pyramid out of cardboard
How to make a pyramid out of cardboard. A tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex.
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Why circles are round (and triangles too!) rotor in a square hole: http://www.youtube.com/watch?v=KUeQugasOkk more info on reuleaux rotors and other SWEET stuff: http://www.howround.com minutephysics is now on Google+ - http://bit.ly/qzEwc6 And facebook - http://facebook.com/minut
From playlist MinutePhysics
Weird Triangle Wheels Roll Like Circles
In this video I show you a triangle wheel called a Reuleaux triangle. Triangle Wheel Bike Video: https://www.youtube.com/watch?v=BeOS9pG6vjU Watch other popular videos from my channel Superhydrophobic Knife Slices Water Drops in Half https://youtu.be/Ls_ISb7lG-I Real-Life Invisibility
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Phase space representation of the billiard in Reuleaux-like pentagons
The billiard in this simulation is obtained by replacing the sides of a regular pentagon by circular arcs. The radius of the arcs varies between the 1 and 10, when measured in terms of the circumradius of the initial pentagon. A genuine "Reuleaux pentagon", similar to the Reuleaux triangle
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How to construct a Tetrahedron
How the greeks constructed the first platonic solid: the regular tetrahedron. Source: Euclids Elements Book 13, Proposition 13. In geometry, a tetrahedron also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. Th
From playlist Platonic Solids