equilateral

You can build hexagons really easily out of equilateral triangles, which seems even purere than squares to me.

On Android this is three dots in an equilateral triangle, with two of three sides connected by a line.

The chord through the midpoints of two sides of an inscribed equilateral triangle cuts a diameter in the golden ratio.

It's easy, if you normalize it so that it sums to one, it drops a dimension, and becomes an equilateral triangle.

An equilateral triangle with the top half removed is not a rhombus, it's a trapezoid.

The equilateral triangle divided into four smaller such triangles, and the square divided into four smaller squares both have advantages as representations.

Now, imagine trying to lay out 5 equilateral triangles in 2D instead of 3D.

Look at his very first proof - the construction of an equilateral triangle.

Draw an equilateral triangle and its altitudes, creating 6 regions inside.

One more UI request: Given two points, there are two possible third points on an equilateral triangle, and no clear way to choose between them.

Kind of an equilateral force balance, with a self stable state that things will naturally gravitate towards if the background energy level is low enough.

Take five equilateral triangles, and attach them together so that they meet at one vertex and the respective sides adjacent to the vertices are shared.

So it’s a new class of equilateral convex polyhedra with icosahedral symmetry, which is interesting because the familiar “geodesic dome” polyhedra are not equilateral.

The paper doesn't make any sense without the title: "Can n^2 + 1 unit equilateral triangles cover an equilateral triangle of side >n, say n+\epsilon?"

This is no different than not being able to easily ask, "Can we construct an equilateral triangle with side lengths of π?" before abstracting from more concrete things into numbers.

I suppose we should state that this will be an equilateral triangle formed between the Earth, Mars, and the Camera, the "height" of the equilateral triangle is x, and that Earth will be so many pixels wide on that camera when zoomed 2000x (or whatever).

Interesting, and according to Wikipedia, first devised in the short story series: Venus Equilateral.