Thursday, December 3, 2015

Cutting A Triangle In Fourths

Consider an equilateral triangle in the xy-plane, centered at the origin.

1) By suitably rotating the triangle about its center, is it possible for each quadrant to contain one fourth of the triangle's area?

2) By suitably rotating the triangle about its center, is it possible for each quadrant to contain one fourth of the triangle's perimeter?

The answer to the area problem can be deduced from the information here. Just for fun, I also made an animation. If it doesn't show as embedded here, you can watch it on YouTube.





Endless loop GIF version:





No comments: