Constant width | Piecewise-circular curves
In geometry, a Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius. These shapes are named after their prototypical example, the Reuleaux triangle, which in turn, is named after 19th-century German engineer Franz Reuleaux. The Reuleaux triangle can be constructed from an equilateral triangle by connecting each two vertices by a circular arc centered on the third vertex, and Reuleaux polygons can be formed by a similar construction from any regular polygon with an odd number of sides, or from certain irregular polygons. Every curve of constant width can be accurately approximated by Reuleaux polygons. They have been applied in coinage shapes. (Wikipedia).
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
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
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
From playlist Particles in billiards
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
From playlist Recent videos
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
From playlist Particles in billiards
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
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
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
Lecture 14: Hinged Dissections
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture introduces adorned chains and slender chains. Proofs involving these definitions, as well as locked polygons and hing
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
What are four types of polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Applying the properties of a rhombus to determine the length of a diagonal
👉 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
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
Phase space representation of billiards interpolating between a circle and a hexagon
In this simulation, I wanted to see what happens when you continuously deform the boundary of a billiard from a circle to a regular hexagon. The billiard in a circle has very regular dynamics (the technical work is "integrable"), because a given trajectory always hits the boundary with the
From playlist Particles in billiards
Using the pythagorean theorem to 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
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
From playlist Amazing 3D Printed Objects
Using the properties of a rhombus to determine the missing value
👉 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