“If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.”
-From the fifth postulate of the Elements.
I have an infinite longing for mathematics. When I was young, I thought little of math because I could not understand its intricacy, but mathematics is the truth that penetrates through all things. Like the principle of the constancy of the velocity of light which is upheld to be true in modern times, solid principles rule over the world of mathematics with absolute power. Aside from being absolute, unsolved problems of mathematics could never be solved unless with a free and flexible thinking—even when the truth may change our unshaken belief in the world and turn it upside down completely.
The foundation of one of the fields of mathematics, geometry, already existed in ancient Greece. The author of the book “Elements”, which sounds so formal, is Euclid. Human race has treated geometry for the most part based on his theory. It’ almost as if his theory was the never-changing absolute truth. His principles and postulates have been questioned and tested countless times for containing contradiction or flaws.
One of his famous postulates that have been challenged is the fifth postulate or so-called the parallel postulate. To jump to the conclusion, this postulate was one day denied. But that is to say that a new way of thinking was formed that differs from the concept of space which was the basis of the postulate. This led to Non-Euclidean geometry, topology and then geometry that we know now.
I found Euclid’s principles and the Elements so appealing that I felt the urge to photograph a shape itself. But a shape of square or color yellow itself do not exist. They do not sell them at Tokyu Hands, and I can’t take a picture of concepts. But at that time, I felt like I saw them clearly. Shapes and colors, and their very nature, felt like they existed in the world. Now, the only proof that was not an illusion is these images.
