Pi value for Circle a

Question

IF I Have Pi value For Circle that mean i have the Ratio between The Circumference and Diameter [by def.]

I noted in lesson of Measuring angles By The Radian Also Pi Value which standards for 180 degree What is The Different between The First Pi and the Second Pi ? are They Related to each other ?

Answer 1

First, let me define what a radian is:

Suppose you have a circle radius $r$. If you measure an angle of $k^c$ ($k$ radians) from the centre, the portion of the circle's edge between the two lines that form your angle will have length $kr$.

Note that $\pi^c=180^0$, thus $2\pi^c=360^0$. So if theoretically you stated that the two radii you were creating the angle between were the same line (i.e. the angle between them was the whole way around the circle - either $360^0$ or $2\pi^c$), the arc created would have length $2\pi r$. This is also the circumference by the way I measured it from the same line, so $$c=2\pi r\therefore c=\pi d \therefore\pi=\frac{c}{d}$$ Does that help?

Answer 2

$\pi$ is the number which represents the ratio of the circumference to the diameter, so a circle of radius $r$ has circumference $2\pi r$. In radian measure, a central angle is measured by the ratio of the length of the arc it subtends to the radius of the circle. So, in a circle of radius $r$ a central angle of $180^{\circ}$ subtends an arc of length $\pi r$ and the radian measure is $$\frac{\pi r}{r}=\pi$$