In geometry, an orthocentric tetrahedron is a tetrahedron where all three pairs of opposite edges are perpendicular. It is also known as an orthogonal tetrahedron since orthogonal means perpendicular. It was first studied by Simon Lhuilier in 1782, and got the name orthocentric tetrahedron by G. de Longchamps in 1890. In an orthocentric tetrahedron the four altitudes are concurrent. This common point is called the orthocenter, and it has the property that it is the symmetric point of the center of the circumscribed sphere with respect to the centroid. Hence the orthocenter coincides with the Monge point of the tetrahedron. (Wikipedia).
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
Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger
In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb
From playlist Universal Hyperbolic Geometry
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
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
What Are Allotropes of Metalloids and Metals | Properties of Matter | Chemistry | FuseSchool
What Are Allotropes of Metalloids and Metals Learn the basics about allotropes of metalloids and metals, as a part of the overall properties of matter topic. An allotrope is basically a different form of the same element, each with distinct physical and chemical properties. For example
From playlist CHEMISTRY
The Three / Four bridge in Triangle Geometry: Incentres and Orthocentres | Six 6 | Wild Egg
We look at how to cross the Three / Four bridge geometrically: in both directions. This connects with some classical triangle geometry, involving triangle centres going back to ancient Greek geometry. We will touch base with the algebraic orientation to angle bisection, modifying a little
From playlist Six: An elementary course in Pure Mathematics
How to find the orthocentre (point of concurrence of altitudes) of a triangle using a traditional compass technique within Inkscape. Visit my website www.maths-pro.com for 100s of free geometry resources.
From playlist Inkscape for teachers
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
AlgTop8: Polyhedra and Euler's formula
We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and the flow down a sphere. This is the eighth lecture in this beginner's
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Triangle Centres (Orthocentre, Centroid & Circumcentre)
More resources available at www.misterwootube.com
From playlist Further Properties of Geometrical Figures
Three dimensional geometry, ZOME, and the elusive tetrahedron
Lectures notes at http://www.maths.unsw.edu.au/seminars/2012-07/three-dimensional-geometry-zome-and-elusive-tetrahedron. The geometry of three dimensional space, despite its obvious importance, is a sadly neglected topic in modern mathematics. One of the reasons is that the topic is rather
From playlist MathSeminars
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
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
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
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
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
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