You can draw a regular pentagon using a compass and a straightedge... or can you? In this video I demonstrate two geometric constructions of pentagons, and then compare them in the context of art and design.
That's why I love Dürer's construction of the regular heptagon inscribed in the unity circle using √3 / 2 (the height of the regular triangle on the radius) as the side length. An even better approximation would be 1 - (4/11)², but the construction would be more prone to errors.
I feel your pain - maths should win! But the world isn't all logic, there are humans in it, and we makes it wonderfully imperfect. I get the same frustration when I want blending of black and white to be balanced - adding 5 % white to black should have the same impact as adding 5 % black to white, but it isn't. The black have a much higher impact as the white have. It's like having the dark force taking over your veins and you are unwillingly becoming a sith lord. For the good side to win it has to reach over 30-40%. It's annoyingly unfair.
