Unit
Circles
Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
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Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
Circumference can be thought of as the "perimeter" of a circle or the distance around a circle. Since pi is the ratio of circumference to diameter, circumference can be calculated by multiplying the circle's diameter by pi. Another formula substitutes d = 2r, where one diameter equals two radii, and C = 2(r)(pi). Related topics include area of a circle, arc length, and parts of a circle.
One of the ways we can separate circles is by talking about their circumference. Different size circles have different size circumferences. But what is circumference? Well a not very technical explanations is that it's the distance around a circle, so if I drew in a little guy right here, the circumference is how far would he have to walk to end up where he started? So it's going to be a distance.
There's a special ratio that the ancient Mathematicians found of circumference to diameter, so that's what we're going to use to discribe circumference. And that ratio was pi, so pi isn't rational number which means if I wrote down its decimal it would non repeating forever and ever. And pi is that ratio, remember a ratio could be be written as a fraction, of circumference to diameter so if I wrote in a radius, remember that if you have 2 radii that equals one diameter, so pi is that ratio in a circle of its circumference to its diameter. If I solve this equation for c that is if I multiplied both sides by d then I could write circumference, capital C, as pi times the diameter, so that's one formula for circumference.
The other says that one diameter is equal to 2 radii, so I can substitute in 2r for d, so the other equation you can use for circumference is pi times 2r so either of these equations when you know one of the variables either the diameter, circumference or radius will allow you to solve for that other missing variable.