🚀 go-pugleaf

Dear Professor,
Please study my simple experiment
I'm sure you will find it very interesting !
I am sure the formula to find Area of a Circle is WRONG.

If we take a common cylinder and squash one end
so that it has the shape of a square, we will have one
end with the Area of a Square and the other end with
the Area of a Circle. Both cross sectional area's will
be of identical value, because we have not removed
or added material.

Lets cut one end off and lay it out flat so that we can
accurately measure the circumference and perimeter.

Measured value = 133 mm
This is both the circumference and perimeter.

Each side of the square =  133 / 4  =  33.25 mm

From this we can calculate the Area of the Square.

Area = base * height

Area  =   33.25 * 33.25  =  1105.5625  mm squared
                                       =========


Now lets calculate the Area of the circle.

Circumference =  Pi * Diameter

Diameter = Circumference / Pi

Diameter of our Circle =  42.33521486 mm

It is commonly thought that the formula to calculate
the Area of a Circle is  =   Pi * Radius Squared

Area of Circle  =     Pi  *  21.16760743  *  21.16760743

Area of the Circle =    1407.645894   mm squared.
                                ===========

============================================
OUR TWO ANSWERS CAME OUT DIFFERENT.
ONE OF THEM IS WRONG !!!!!!!
============================================


The correct formula to calculate Area of a Circle

                                Circumference squared
Area of Circle   =    ----------------------------------
                                            Sixteen

                               pi squared * diameter squared
Area of Circle  =     ---------------------------------------
                                                16

Area of a Circle  is
Circumference squared divided by Sixteen.

                              133  *  133
Area of Circle  =   ------------------      =    1105.5625  mm squared
                                     16                    =========

Using this formula we get the correct answer for
Area of a circle, and it work's perfectly for all Circle's.

Area of a Circle   =     C/4  *  C/4     =      (C/4)squared
                Area   =    Base * Height

All of the common formula's for Area and Volume
will need to be revised.

Thank you very much for looking at my experiment.
Please tell me what you think.