Where did the formula for area of a circle come from?
multipleQAs
Where and from who did the formula for area of a circle come from? Where did Archimedes derive the formula for area of a circle come from? From what literary work did the formula for area of a circle first come from?
Archimedes
viewing the circle as the limit of a sequence of regular polygons method of exhaustion,
The Measurement of a Circle
Area of a circle
Where did the formula for area of a circle come from?
Area of a circle Squaring the circle Area Circle Circular sector Pi Apothem Circumference Heron's formula Cyclic quadrilateral
In geometry, the <b>area</b> enclosed by a <b>circle</b> of radius r is π r<sup>2</sup>. Here the Greek letter 
π represents a constant, approximately equal to 3.14159, which is equal to the 
ratio of the circumference of any <b>circle</b> to its diameter. One method of deriving this 
<b>formula</b>, which originated with Archimedes, ... of the lune of Hippocrates, but <b>did</b> 
not identify the constant of proportionality. Squaring the circle is a problem proposed by ancient geometers. It is the 
challenge of ... Archimedes proved the <b>formula</b> for the <b>area of a circle</b> (A = πr<sup>2</sup>, 
where r is the ... Gelder <b>did</b> not construct the side of the square, it was enough for 
him to find the ... attempts at circle-squaring had <b>come</b> to be seen as &quot;wild and 
fruitless&quot;:. ... the first to show that the <b>area</b> of a disk (the region enclosed by a <b>circle</b>) ... the 
polygon&#39;s <b>area</b> got closer and closer to that of the <b>circle</b> (and <b>did</b> ... π is 
transcendental (not the solution of any polynomial <b>equation</b> with&nbsp;... A <b>circle</b> is a shape consisting of all points in a plane that are a given distance 
from a given point ... The <b>circle</b> is the plane curve enclosing the maximum <b>area</b> 
for a given arc ... This <b>equation</b>, known as the <b>Equation</b> of the <b>Circle</b>, follows from 
the ... However, this equivalence between L1 and L∞ metrics <b>does</b> not 
generalize to&nbsp;... A circular sector or <b>circle</b> sector (symbol: ⌔), is the portion of a disk enclosed by 
two radii and an arc, where the smaller <b>area</b> is known as the minor sector and&nbsp;... The number π is a mathematical constant. Originally defined as the ratio of a 
<b>circle</b>&#39;s circumference to its diameter, it now has various equivalent definitions 
and appears in many <b>formulas</b> in all <b>areas</b> of mathematics and physics. ... 
Although the simple continued fraction for π (shown above) also <b>does</b> not exhibit 
any other&nbsp;... The apothem of a regular polygon is a line segment from the center to the 
midpoint of one of its ... The apothem a can be used to find the area of any 
regular n-sided polygon of side length s according to the ... This property can also 
be used to easily derive the <b>formula</b> for the <b>area of a circle</b>, because as the 
number of sides&nbsp;... In geometry, the circumference of a <b>circle</b> is the (linear) distance around it. That is
, the ... The above <b>formula</b> can be rearranged to solve for the circumference: ... a 
<b>Circle</b> written circa 250 BCE, Archimedes showed that this ratio (C/d, since he <b>did</b> 
not use the name π) was greater ... &quot;Perimeter, <b>Area</b> and Circumference&quot; (PDF). Heron&#39;s <b>formula</b>. From Wikipedia, the free encyclopedia. Jump to navigation 
Jump to search. This article is about calculating the <b>area</b>&nbsp;... The <b>formulas</b> and properties given below are valid in the convex case. The word 
cyclic is from the Ancient Greek κύκλος (kuklos) which means &quot;<b>circle</b>&quot; or &quot;wheel&quot;.
Archimedes
Area of a circle