Draw a Circle of Radisu R Centered at the Origin

A circumvolve is a round, two-dimensional shape. All points on the edge of the circle are at the same distance from the center.

The radius of a circle is a line from the heart of the circumvolve to a betoken on the side. Mathematicians use the letter of the alphabet ${\displaystyle r}$ for the length of a circumvolve's radius. The heart of a circle is the bespeak in the very middle. It is oftentimes written as :).

The diameter (meaning "all the way across") of a circumvolve is a straight line that goes from 1 side to the reverse and right through the center of the circle. Mathematicians use the letter ${\displaystyle d}$ for the length of this line. The diameter of a circle is equal to twice its radius ( ${\displaystyle d}$ equals 2 times ${\displaystyle r}$ ):^[1]

${\displaystyle d=2r}$

The circumference (significant "all the way around") of a circle is the line that goes around the center of the circumvolve. Mathematicians use the letter of the alphabet ${\displaystyle C}$ for the length of this line.^[two]

The number π (written equally the Greek letter of the alphabet pi) is a very useful number. It is the length of the circumference divided by the length of the diameter ( ${\displaystyle \pi }$ equals ${\displaystyle C}$ divided by ${\displaystyle d}$ ). Equally a fraction the number ${\displaystyle \pi }$ is equal to about ${\displaystyle 22/7}$ or ${\displaystyle 355/113}$ (which is closer) and as a number it is about 3.1415926535.

The expanse of the circumvolve is equal to ${\displaystyle \pi }$ times the area of the grayness foursquare.

The surface area, ${\displaystyle A}$ , inside a circle is equal to the radius multiplied by itself, and then multiplied by ${\displaystyle \pi }$ ( ${\displaystyle A}$ equals ${\displaystyle \pi }$ times ${\displaystyle r}$ times ${\displaystyle r}$ ).

${\displaystyle A=\pi r^{2}}$

Calculating π [change | modify source]

${\displaystyle \pi }$ can be measured past drawing a circle, then measuring its diameter ( ${\displaystyle d}$ ) and circumference ( ${\displaystyle C}$ ). This is because the circumference of a circumvolve is always equal to ${\displaystyle \pi }$ times its bore.^[1]

${\displaystyle \pi ={\frac {C}{d}}}$

${\displaystyle \pi }$ tin can too be calculated by only using mathematical methods. Most methods used for calculating the value of ${\displaystyle \pi }$ take desirable mathematical properties. However, they are hard to sympathise without knowing trigonometry and calculus. However, some methods are quite simple, such as this form of the Gregory-Leibniz series:

${\displaystyle \pi ={\frac {4}{1}}-{\frac {four}{3}}+{\frac {four}{5}}-{\frac {iv}{7}}+{\frac {four}{9}}-{\frac {four}{xi}}\,\ldots }$

While that series is easy to write and calculate, it is not easy to see why it equals ${\displaystyle \pi }$ . A much easier way to approach is to describe an imaginary circumvolve of radius ${\displaystyle r}$ centered at the origin. Then any bespeak ( ${\displaystyle x}$ , ${\displaystyle y}$ ) whose distance ${\displaystyle d}$ from the origin is less than ${\displaystyle r}$ , calculated by the Pythagorean theorem, volition be within the circle:

${\displaystyle d={\sqrt {x^{two}+y^{ii}}}}$

Finding a set of points inside the circle allows the circle'south area ${\displaystyle A}$ to be estimated, for case, by using integer coordinates for a big ${\displaystyle r}$ . Since the expanse ${\displaystyle A}$ of a circumvolve is ${\displaystyle \pi }$ times the radius squared, ${\displaystyle \pi }$ tin be approximated by using the following formula:

${\displaystyle \pi ={\frac {A}{r^{2}}}}$

Calculating the surface area, circumference, diameter and radius of a circle [change | modify source]

Area [change | change source]

Using its radius: ${\displaystyle A=\pi r^{2}}$

Using its diameter: ${\displaystyle A={\frac {\pi d^{2}}{4}}}$

Using its circumference: ${\displaystyle A={\frac {C^{ii}}{four\pi }}}$

Circumference [change | alter source]

Using its diameter: ${\displaystyle C=\pi d}$

Using its radius: ${\displaystyle C=2\pi r}$

Using its area: ${\displaystyle C=2{\sqrt {\pi A}}}$

Bore [alter | change source]

Using its radius: ${\displaystyle d=2r}$

Using its circumference: ${\displaystyle d={\frac {C}{\pi }}}$

Using its area: ${\displaystyle d=2{\sqrt {\frac {A}{\pi }}}}$

Radius [alter | change source]

Using its diameter: ${\displaystyle r={\frac {d}{2}}}$

Using its circumference: ${\displaystyle r={\frac {C}{ii\pi }}}$

Using its area: ${\displaystyle r={\sqrt {\frac {A}{\pi }}}}$

[modify | change source]

• Semicircle
• Sphere
• Squaring the circle
• Pi
• Pi (letter)
• Tau

References [change | modify source]

1. ↑ ^{i.0 1.ane} Weisstein, Eric W. "Circumvolve". mathworld.wolfram.com . Retrieved 2020-09-24 .
2. ↑ "Basic information about circles (Geometry, Circles)". Mathplanet . Retrieved 2020-09-24 .

Other websites [change | alter source]

Wikimedia Commons has media related to Circumvolve .

• Calculate the measures of a circle online Archived 2007-09-28 at the Wayback Machine

conwayreateromir.blogspot.com

Source: https://simple.wikipedia.org/wiki/Circle

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