Euclid's Muse

Creating a tangent on a circle given point A that is outside the circle.

This proposition proves that line AD is longest, ED is shorter, FD is shorter than ED, and CD is even shorter.and that for any line there is only one other line with a point on the circle and a point at D that is equal. (Unless you drag it to somewhere it’s not supposed to be)

I like it because it’s colorful.

Creating a parallelogram equal to a given quadrilateral with a given angle.

The very first proposition, in which Euclid creates a equilateral triangle from a straight line by using two circles.

Can you create a regular pentagon without a protractor? Because it’s pretty impressive how Euclid did it with only a compass and a ruler.

Note that the yellow triangle is similar to the one inside the pentagon.

One of my favorite apps because it looks deceptively simple, but takes some really creative thinking.

This app creates a square (in red) that has the same area as a given quadrilateral.

Skipping straight ahead to book 4 (shh this one is actually a first draft)

Although GeometryExpressions allows you to create polygons with anywhere from 3 to 100 sides, Euclid gives us a way to create a regular hexagon that doesn’t need such fancy technology.

To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.

In other words, given angle D and triangle ABC (in blue), construct a parallelogram (in yellow) that has an equal area to triangle ABC.

The famous Pythagorean Theorem. Can you see how it works?

This app shows how to create a triangle when you’re given a line composed of lines A, B, and C.