How To Actually Make Parallel Lines Intersect
An introduction to projective geometry!
How can parallel lines intersect if they are by definition supposed to maintain a constant width? This very notion sounds absurd. Yet, it is not only practically possible, but is also a necessity in mathematics and science.
In this essay, we will start with the historical development of the science behind optics and discover how this flows into the notion of intersecting parallel lines. Following this, we will explore practical applications of this concept as well. Let us begin.
How Does Vision Work?
The notion of light rays bouncing off of objects and registering inside our eyes is a relatively recent one. What’s more, this is NOT a very intuitive concept. The proof for this is in the history pudding.
Many prominent people of science such as Plato and the Pythagoreans argued that sight is achieved by a fire-like phenomenon within our eyes. There were also other competing speculative theses about how our eyes produce light.
The theory of vision involving reflected light rays was first documented by Cairene mathematician Abu ‘Ali al-Hasan ibn al-Haytham in his optics book, Kitab al-Manazir.
