by Prof. Mahesh Sharma, Center for Teaching and Learning Mathematics

300 years BCE. a Greek mathematician named Euclid, compiled and organized all of the knowledge of science, mathematics, and geometry into 13-volumes called, "Elements", while living and working in Alexandria, Egypt. Euclid created a framework for deductive logical reasoning, beginning with definitions and a list of assumptions called postulates. Euclid's work has been studied for over 2,326 years.

Arithmetic focuses on operations on numbers.

Geometry focuses on defining spatial sense and object attributes. We describe spatial observations with numbers.

Thousands of years ago, in India, a man noticed that the tree outside his hut cast a shadow, that seemed to move from one day to another. He was curious, so each day, at the same time, he marked the location of the shadow with a pebble. He noticed that the shadow was forming an arc and eventually formed a circle around the tree. When the circle was complete, he counted the pebbles and found that there were 360.

From this, he deduced that there were 360 days in a year. This is the beginning of imposing a number on space.

One complete rotation around the tree was 360 pebbles, which formed a complete circle. This is the origin of saying the perimeter of a circle measures 360 degrees, and half of a circle is 180 degrees. The straight line that cuts the circle in half measures 180 degrees. And a perpendicular line that cuts that line in half would create an angle or corner measuring 90 degrees.