Our calculator is designed to help with a common geometry textbook problem, finding the x/y coordinates on the face of a circle. There are other functions as well, mapping out diameter, circumference, and area from a given radius. Dive into our complex little world of the circle below!
Formula for Equation of the Circle
Let (A,B) equal the center coordinates of the circle on a Cartesian plane. The process for describing all the points on the face of the circle is:
(x - A)^2 + (y - B)^2 = r^2
Where r is the radius. Given the constants of the circle, you can find any x/y position on the circle's face.
A circle can also be prescribed by the formulas:
x = r * cos(P)
y = r * sin(P)
Where x/y or the Cartesian coordinates of any point on the circle, r is the radius, and P is the parameter. These formulas use trigonometry in the form of our familiar Pythagorean theorem. Formally, it states that the radius is the hypotenuse of a right-angle (90-degrees) triangle whose other sides are of length (x - A) and (y - B).
There are many specialized terms in mathematics to refer to different portions of and aspects of a circle:
• Chord - any line drawn crossing the circle from one lip of the perimeter to another.
• Secant - a continuous line passing through the circle.
• Tangent - a continuous line which touches the perimeter of the circle at one point.
• Radius - the distance from the center to the perimeter.
• Diameter - the distance across the circle at the center point.
• Arc - a portion of the circle's perimeter.
• Sector - a wedge cut from the circle, like a slice of pie.
• Segment - a chunk cut from the circle by a straight line.
• Disc - the region of space covered by the circle, plus the circle.
The basic Equation of the Circle can help with defining any of these points or portions.
The Allure of the Circle
The humble circle has been a geometric shape which has fascinated scientific minds for all of history.
Because circles are, of course, found everywhere in nature, from bubbles to fruit to the shape of the sun and moon, circles were held to be of mystical significance. The irrational number Pi was a puzzle for centuries, first being computed by an infinite series of multi-sided polygons. A triangle is not shaped at all like a circle, but a hexagon starts to resemble it; projecting from increasingly rounder edged polygons was a popular method for estimating Pi.
Estimating Pi is still the best way to deal with it since we can't know its absolute, complete value.
Even though memorizing Pi to many decimal places is a popular stunt to show off one's memory, mathematicians have proved that just the first eight decimal places of Pi (3.14159265) is enough precision that you could use it to construct a hoop around the entire Earth at any point and be off by as little as a centimeter!