Arithmetic problems of solid geometry | Polyhedra

Heronian tetrahedron

A Heronian tetrahedron (also called a Heron tetrahedron or perfect pyramid) is a tetrahedron whose edge lengths, face areas and volume are all integers. The faces must therefore all be Heronian triangles.Every Heronian tetrahedron can be arranged in Euclidean space so that its vertex coordinates are also integers. (Wikipedia).

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Regular polyhedra

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

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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

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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.

From playlist HOME OF GREENPOWERSCIENCE SOLAR DIY PROJECTS

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4 DIFFERENT ways to prove Heron's formula

Your high school Math(s) teacher might not even explain to you how Heron's formula is derived, let alone Heron's original idea. This video explains 4 different ways to prove the Heron's formula. Note: This is a sort of experiment for longer videos. I am not exactly sure whether this wou

From playlist Geometry Gem

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Trigonometry XII: Heron's Formula for the Area of Triangle

Follow me on instagram @whatthehectogon https://www.instagram.com/whatthehectogon/ If you have any questions, leave a comment below or feel free to email me at the misspelled whatthehectagon@gmail.com In this video, I prove the lovely formula for the area of a triangle from the indomitab

From playlist Trigonometry

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How to Construct a Dodecahedron

How the greeks constructed the Dodecahedron. Euclids Elements Book 13, Proposition 17. In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. A regular dode

From playlist Platonic Solids

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Superhero Triangles - Numberphile

Heronian triangles and other fascinating things, featuring Dr James Grime. Get your Superhero Triangle T-Shirt and other stuff: http://bit.ly/Super_Tri More links & stuff in full description below ↓↓↓ More videos with Dr Grime: http://bit.ly/grimevideos Dr James Grime: https://www.singing

From playlist James Grime on Numberphile

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Canonical structures inside the Platonic solids III | Universal Hyperbolic Geometry 51

The dodecahedron is surely one of the truly great mathematical objects---revered by the ancient Greeks, Kepler, and many mathematicians since. Its symmetries are particularly rich, and in this video we look at how to see the five-fold and six-fold symmetries of this object via internal str

From playlist Universal Hyperbolic Geometry

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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

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Advancing Cellular Life | Astrobiology Course 5.1

Learn the foundations of astrobiology from Professor Impey, a University Distinguished Professor of Astronomy at the University of Arizona, with our Astrobiology: Exploring Other Worlds course here on YouTube. This video is part of module 5, Complex Life & Intelligence. Want to take the f

From playlist Astrobiology Course Module 5: Emerging Life & Intelligence

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Sierpinski from Pascal

This is a recreation of a short clip from a long form video showing six different ways to construct the Sierpinski triangle: https://youtu.be/IZHiBJGcrqI In this short, we shade odd entries of the Halayuda/Pascal triangle to obtain the Sierpinski triangle. Can you explain why this works?

From playlist Fractals

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2003 AIME II problem 4 (part 1) | Math for fun and glory | Khan Academy

Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/math/math-for-fun-and-glory/aime/2003-aime/v/2003-aime-ii-problem-4-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=mathforfunandglory Missed the previous lesson? https://www.khanacademy.org/math/math-for-fun-and-g

From playlist AIME | Math for fun and glory | Khan Academy

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Three dimensional geometry, Zome, and the elusive tetrahedron (Pure Maths Seminar, Aug 2012)

This is a Pure Maths Seminar given in Aug 2012 by Assoc Prof N J Wildberger of the School of Mathematics and Statistics UNSW. The seminar describes the trigonometry of a tetrahedron using rational trigonometry. Examples are taken from the Zome construction system.

From playlist Pure seminars

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Average height | MIT 18.02SC Multivariable Calculus, Fall 2010

Average height Instructor: Joel Lewis View the complete course: http://ocw.mit.edu/18-02SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.02SC: Homework Help for Multivariable Calculus

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The Tetrahedral Boat - Numberphile

Featuring Marcus du Sautoy discussing polyhedra and the art of Conrad Shawcross... More links & stuff in full description below ↓↓↓ Marcus du Sautoy website: https://www.simonyi.ox.ac.uk Marcus' books on Amazon: https://amzn.to/33YbOxS More videos with Marcus: https://bit.ly/Marcus_Number

From playlist Marcus Du Sautoy on Numberphile

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Regular triangulation of H³

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/nicy. Tiling of H^2 image from http://en.wikipedia.org/wiki/File:H2checkers_iii.png

From playlist 3D printing

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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

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Platonic and Archimedean solids

Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV

From playlist 3D printing

Related pages

Elliptic curve | Irrational number | Tetrahedron | Right triangle | Integer | Trirectangular tetrahedron | Schläfli orthoscheme | Sums of powers | Euclidean space | Heronian triangle | Leonhard Euler | Pythagorean triple | Disphenoid | Isosceles triangle | Euler brick