Archimedes (287-212 BC) was the first to estimate π rigorously. He realized that its magnitude can be bounded from below and above by inscribing circles in regular polygons and calculating the outer and inner polygons' respective perimeters. By using the equivalent of 96-sided polygons, he proved that 310/71< π < 31/7. The average of these values is about 3.14185.
There is an infinite amount of polygons.
Archimedes found a method for finding good approximations to the ration of the circumference of a circle to the diameter. He did this by inscribing polygons inside the circle and finding how the perimeter changes when the number of sides is doubled. Archimedes came up with an approximation that is equivalent to saying that pi is between 3 1/7 and 3 10/71. This is quite far from being as accurate as what you showed.
Polygons are flat shapes with many sides
these polygons arent similar one is turned sideways... * * * * * Don't know which polygons but turning sideways does not affect similarity
The polygons are said to be similar.
umm im noot 100% sure but i am pretty sure its pythagoras or Euclid
It was Archimedes.
Historically one of the early methods of estimating the value of π was by taking a circle and inscribing and circumscribing a regular polygon (constructing a regular polygon inside and outside the circle- they knew how to do that mathematically 500 BC in Greece for a great number of polygons) They took the average of the circumferences of the polygons and divided that by the average of the diameters of the polygons to approximate a value for π.
The ancient Greeks certainly used calculus. Archimedes used regular polygons inscribed and circumscribing a circle to estimate the value of pi. The perimeter of the circle (the circumference) lay between the perimeters of the two sets of polygons. The limit, as the number of sides of the polygon were increased, gave pi. Unfortunately, calculations of trigonometric ratios were not sufficiently refined for Archimedes to get very accurate results.
He calculated the perimeters of regular polygons inscribed within a unit circle and circumscribing the circle (outside the circle). The first is always less than the circumference of the circle ( = 2*pi) and the second is always more. As you increase the number of sides of the polygons, the polygons get closer and closer to the circle and their perimeters get nearer to the circumference.
One mathematician who made significant contributions to areas related to circles is Archimedes. He is known for his discovery of the relationship between the circumference and diameter of a circle, which is now known as π (pi). Archimedes also developed methods to approximate the area enclosed by a circle using polygons, a technique now known as the method of exhaustion.
Archimedes created the formula for measuring the circumference of a circle he used many-sided polygons, both inside and out to approximate it.
There are lots of different types of polygons Polygons are classified into various types based on the number of sides and measures of the angles.: Regular Polygons Irregular Polygons Concave Polygons Convex Polygons Trigons Quadrilateral Polygons Pentagon Polygons Hexagon Polygons Equilateral Polygons Equiangular Polygons
A football has a curved surface and polygons are flat. You can approximate a curved surface quite well if you use enough polygons but each polygon will still be flat and a football does have a curved (and rough) surface. Using a few thousand polygons you can create an approximation of a football with stitching seams and every detail but you will not have a curved surface you will have an approximation of a curved surface.
All polygons and polyhedra.All polygons and polyhedra.All polygons and polyhedra.All polygons and polyhedra.
That is because an octagon is singular and polygons is plural. An octagon is a polygon, and octagons are polygons but a octagon cannot be a polygons.
regular polygons are the ones that all sides are equal