In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube. It can be seen as an octahedron with triangular pyramids added to each face; that is, it is the Kleetope of the octahedron. It is also sometimes called a trisoctahedron, or, more fully, trigonal trisoctahedron. Both names reflect that it has three triangular faces for every face of an octahedron. The tetragonal trisoctahedron is another name for the deltoidal icositetrahedron, a different polyhedron with three quadrilateral faces for every face of an octahedron. This convex polyhedron is topologically similar to the concave stellated octahedron. They have the same face connectivity, but the vertices are in different relative distances from the center. If its shorter edges have length 1, its surface area and volume are: (Wikipedia).
Arctan(1) + Arctan(2) + Arctan(3) = π
From playlist Trigonometry TikToks
From playlist Trigonometry TikToks
Trigonometry for Beginners || Trigonometry Basics
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. This math video tutorial provides a basic introduction into #trigonometry. It covers trigonometric functions, ratios such as sine, cosine, and tangent, converting polar coordin
From playlist Trigonometry
Using pythagorean identities to help me verify an identity
👉 Learn how to verify Pythagoras trigonometric identities. A Pythagoras trigonometric identity is a trigonometric identity of the form sin^2 (x) + cos^2 (x) or any of its derivations. To verify trigonometric expression means to verify that the term(s) on the left-hand side of the equality
From playlist Verify Trigonometric Identities
Verify an identity using the pythagorean identities
👉 Learn how to verify Pythagoras trigonometric identities. A Pythagoras trigonometric identity is a trigonometric identity of the form sin^2 (x) + cos^2 (x) or any of its derivations. To verify trigonometric expression means to verify that the term(s) on the left-hand side of the equality
From playlist Verify Trigonometric Identities
Using the Pythagorean identity to verify an identity
👉 Learn how to verify Pythagoras trigonometric identities. A Pythagoras trigonometric identity is a trigonometric identity of the form sin^2 (x) + cos^2 (x) or any of its derivations. To verify trigonometric expression means to verify that the term(s) on the left-hand side of the equality
From playlist Verify Trigonometric Identities
From playlist Trigonometry TikToks
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/19O1
From playlist 3D printing
Math Mornings at Yale: Asher Auel - Wallpaper, Platonic Solids, and Symmetry
The Platonic solids-the tetrahedron, cube, octahedron, dodecahedron, and icosahedron-are some of the most beautiful and symmetric geometrical objects in 3-dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geom
From playlist Math Mornings at Yale
Journée de la Revue d’histoire des mathématiques - Veronica Gavagna - 01/12/17
Journée de la Revue d’histoire des mathématiques (séance préparée par la rédaction de la RHM) Veronica Gavagna (Università degli Studi di Firenze), « Studies on regular polyhedra in the Renaissance: the case of Francesco Maurolico » ---------------------------------- Vous pouvez nous re
From playlist Séminaire d'Histoire des Mathématiques
See http://thedicelab.com/ for more details. These dice are available at http://www.mathartfun.com/shopsite_sc/store/html/DiceLabDice.html
From playlist Dice
Tetrahedron decomposition (pure CSS 3D)
You can see the live demo here https://codepen.io/thebabydino/pen/OjgWQG/ If the work I've been putting out since early 2012 has helped you in any way or you just like it, please consider supporting it to help me continue and stay afloat. You can do so in one of the following ways: * yo
From playlist CSS variables
How to construct an Octahedron
How the greeks constructed the 2nd platonic solid: the regular octahedron Source: Euclids Elements Book 13, Proposition 14. In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Plat
From playlist Platonic Solids
Unique way to divide a tetrahedron in half
This is an interesting geometry volume problem using tetrahedrons. We use the volume of a tetrahedron and Cavalieri's principle in 3D.
From playlist Platonic Solids
Scott Kim - Motley Dissections - G4G13 April 2018
This talk discusses motley dissections — polygons cut into polygons and polyhedra cut into polyhedra such that no two pieces every completely share an edge or a face. The most famous motley dissection is the squared square. My contribution extends this to triangled triangles, pentagoned pe
From playlist G4G13 Videos
Use pythagorean identities to verify an identity
👉 Learn how to verify Pythagoras trigonometric identities. A Pythagoras trigonometric identity is a trigonometric identity of the form sin^2 (x) + cos^2 (x) or any of its derivations. To verify trigonometric expression means to verify that the term(s) on the left-hand side of the equality
From playlist Verify Trigonometric Identities
Perfect Shapes in Higher Dimensions - Numberphile
Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions. More links & stuff in full description below ↓↓↓ Extra footage (Hypernom): https://youtu.be/unC0Y3kv0Yk More videos with with Carlo: http://bit.ly/carlo_videos Edit and animation by Pete McPartlan Pete
From playlist Carlo Séquin on Numberphile