Circles and Pi Vocabulary

Fundamental vocabulary terms and mathematical relationships regarding circles, diameter, radius, and the constant pi based on lecture notes.

Diameter ($d$)

The distance all the way across a circle, from one edge to the other, passing through the center.

Radius ($r$)

The distance half way across the circle, from the center to the edge.

Circumference ($C$)

The distance around the circle, which can be thought of as the perimeter of the circle.

Radius Relationship to Diameter

The radius is half the diameter, calculated as $r = \frac{d}{2}$. For example, if the diameter is $10\,cm$, the radius is $5\,cm$.

Diameter Relationship to Radius

The diameter is twice the radius, calculated as $d = 2 \times r$. For example, if the radius is $12\,mm$, the diameter is $24\,mm$.

Pi ($\pi$)

The ratio of the circumference of a circle to the diameter, which always simplifies to an approximation of $3.14$.

Ratio of Circumference to Diameter ($\frac{C}{d}$)

The mathematical relationship that determines the value of Pi ($\pi$); for instance, a cookie with an $18.84\,inch$ circumference and a $6\,inch$ diameter results in a ratio of $3.14$.