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 app uses a physical model to find the largest area triangle whose vertices lie on a smooth closed curve (defined by the red control points).
The triangle defined by the tangent lines at the vertices is displayed, along with its medians.
What do you notice about the maximum?
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.
Create a triangle which has 3 points on the circumference of an ellipse, and two sides passing through the foci. Look at 2 curves formed by the third side: the locus of its center and its envelope. One is an ellipse, the other is not.