CIRCLE
Definition
A circle is a 2D shape that has a closed curve consisting of all points at a FIXED distance from its center.
INTERESTING FACTS:
- A circle is a special kind of ellipse.
It Is Helpful To Think
It is helpful to think of a CIRCLE as a SQUARE that has:
- lost its "edges",
- "rounded" its corners or
- "dropped" some weight.
Traditional Formula
AreaCircle = πr2 or 3.14 x radius2 or
AreaCircle = ¼π x diameter2
NOTE: Pi (π) is the ratio of the circumference of any circle to its diameter or better stated "the circumference divided by its diameter (circumference/diameter)." It is always 3.141592654...
Thinking Inside The Box
If you place a CIRCLE inside of a box (a square but NOT a rectangle), you can easily recognize the horizon and vertical circle's diameters (blue arrows) are the same as the height and width of the square (red arrows).
Diameter is the distance across a circle through its center.
Radius is half of the circle's diameter.
Circumference (from Latin circumferentia, meaning "carrying around") is the linear distance around the edge of a closed curve or circular object — Wikipedia. The formula is: C = πr or 3.1415 x radius.
Ratio is the relation between two similar numbers with respect to the number of times the first contains the second. In the case of a circle, the ratio is between the circumference and diameter. If the diameter is one, you would have to "stretch" 3.14 diameter lengths around a circle to cover the distance of its circumference. If the diameter is two, you would have to "stretch" 6.28 diameter lengths (6.28/2 = 3.1415). The ratio is always Pi (π) or 3.1415 regardless of the size of the circle.
Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve — Wikipedia.
If you further take notice, you will recognize the circle's area is almost the same as the square area except for the four small edge areas (highlighted in yellow). Notice that the smaller the circle the better it is the see that it is almost the area of a square.
If you were to perform calculations on the circle and the square, you will discover the circle's area is about 78.9% (approx. 80%) of the square's area with the four edges making up about 5% each or 20% total.
While it is harder to see the square units like the other 2D shapes (quadrilateral or triangle) because it is a circle and not a square, the above example makes up about 29 of the 36 squares or eighty percent of 36 (0.80 x 36 = 28.8).
KEY: If you wanted to determine the area of a circle, multiply the circle's diameter by itself (since you now know the height and width of a circle in a square is the same as a circle's diameter) and then multiply the result by 0.8 (80%) to get an estimate of the area of the circle.
Example
A circle with a diameter of 6 in has an area of:
- Treat the diameters as both the height and the width.
- Multiply the diameter by itself (6 x 6) or 36 to get the total area of the square around the circle.
- Multiply the total area of the square by 0.80 (80%) to get an approximate area of the circle
or - Subtract 20% from total (.20) area of the square to get an approximate area of the circle.
AreaCircle is approximately 36 x 0.80 = 28.8 in2 or
AreaCircle is approximately 36 - (.20 x 36) = 36 - 7.2 = 28.8 in2.
REFERENCE: See screenshots above for graphic representations.
Memorization Tip
Since a circle is in a "circle" or class my itself, there is only one type of circle and it does not compare to any of the other 2D shapes, there is no need for a memorization tip.