- Home
- Tags
- Random Facts
- Latest Facts

Circle always possess the largest area for the given perimeter of any two dimensional shape.

Lets consider the shape of circle, square, ellipse, octagon having the same perimeter. Let us consider perimeter to be 10.

This can be found by substituting in algebraic terms.

Area of the circle is pi.r^{2} where r = p/(2xpi) , r = 10 / (2 x 3.14) =10/(6.28) = 1.59

substituting in the equation pi.r^{2} = 3.14 x (1.59)^{2}= 3.14 x 2.52 = **7.9**

Area of the square is s^{2}, s= p^{2}/16 , = 10^{2} /16 = 100 / 16 = **6.2**

Area of the octagon is (2 + 2√2)s^{2}, S = p^{2}/64

So the area of an octagon is (2 + 2√2)p^{2}/64

When substituting the values of perimeter, (2 + 2√2) 10^{2}/64 = **7.5**

Area of the octagon is = **7.5**

Thus the result clearly proves that circle will always have the largest area with any two dimensional shape having the same perimeter.

We would often think that there are more number of natural numbers than the even numbers because nat...

If this is proved to be correct, everything we have learned in our life so far in Mathematics will g...

This will be one of the world most unexplained phenomena you would ever see. The miracle of numbers ...

Percy Spencer, an American Engineer accidentally discovered Microwave Oven while working on Raytheon...

The number of possibility chess moves after the white move's is 20 (ie 4 knight moves and 16 moves o...

A Beautiful Mind is the movie based on the life of john nash, who is said to be Nobel Laureate in e...

Your twin sibling will get more youthful than you when he returns from the space travel. If your twi...

Grigori Yakovlevich Perelman is a Russian mathematician, who made a history in Riemannian geometry a...

Daily Maths Topic Today - largest area by shape.