Math & Vitruvian man
The Vitruvian Man By Leonardo Da Vinci ranks among arts most famous work. It is a sketch that would define beauty and change the landscape of art in its time. Man is a symbol of God’s greatest creation. Sketched inside of a square inscribed in a circle it is not difficult to find the underlying mathematics. The palm is the size of 4 fingers. A cubit the size of 6 palms, 4 cubits makes the man and a pace is 4 cubits. Da Vinci displayed simple dimensions demonstrating the beauty of proportions. At first glance the problem is to solve an age old question of squaring a circle. Since we know that the square has an length of 4 cubits and a height of 4 cubits, it is a perfect square. Also the circle is radius 2 and has its center at the navel of the man’s body. At the time of the drawing it was not known that squaring a circle would be impossible since it wasn’t until 1882 that pi was proven to be transcendental. Leonardo took his best shot at squaring a circle using the proportions of the human body.
The problem is based on Euclid’s elements of constructing a circle and square with compass and straightedge. Using a compass and straightedge and Euclid’s first postulate you can begin Leonardo’s famous sketch yourself. Leonardo was attempting to square a circle, that is, he was trying to create a square with the same area as a circle. Using a compass and straightedge to create the sketch, he would have been using the same techniques available to any group of students. Euclid’s postulate 3 and proposition 11 are two proofs to the creations of a square and circle using Euclid’s Elements.
Here are two videos that go deeper into the mathematics behind all this. Enjoy!