The discovery of the circle has definatly enhanced civilization as a whole. The concept of a wheel, the utilization of gears and the simplified ezplanations of the universe awould all be impossible without this shape. Unfourtunalty, amature mathematicians most easily make a fool of themselves when the forget the properties of this shape, as they are extremely prevelant in all mathematics ( from geometry to partial differential equations)
So I would advise anyone, no matter how much math they plan to finish, to commit three details of the circle to memory.
1) the Area of a Circle:
the area of a circle is pi times the radius squared. (the radius is half the diameter, and if you dont know what diameter is… well you will have to look that up yourself)
2) the Circumference of a Circle:
the Circumference (or the perimeter) is equal to the radius times the radius times 2.
3) the Catesian expression of a circle (or the equation of a Circle)
The equation for a circle is: (x-a)^2 +(y-b)*2=r^2
where a and b are the x and y coordinates for the center and r is the radius.