Wonder of SquareShenghang Wang

Units for Area

square meters (m2),

square centimeters (cm2),

square millimeters (mm2),

square kilometers (km2),

square feet (ft2),

square yards (yd2),

square miles (mi2), and so forth.

Algebraically, these units can be thought of

as the squares of the corresponding length units.

Pixels

Calculus

The area of a Trapezoid

The Area of a Circle

The Area of a Circle II

Rectangle

Trigonometric Functions

Projectile motion

Euler’s formula

Logarithmic Spiral

= 1. 4 1 4 2 1, 3 5 6 2 3, 7 3 0 9 5, 0 4 8 8 0, 1 6 8 8 7, 2 4 2 0 9, 6 9 8 0 7, 8 5 6 9 6, 7 1 8 7 5, 3 7 6 9 4, 8 0 7 3 1, 7 6 6 7 9, 7 3 7 9 9, 0 7 3 2 4, 7 8 4 6 2, 1 0 7 0 3, 8 8 5 0 3, 8 7 5 3 4, 3 2 7 6 4, 1 5 7 ……

1

1

Irrational Square Roots

1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799…

= 1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799…

Irrational Square Roots

1

21.73205080756887729352744634150587236694280525381038062805580…

= 1.73205 08075 68877 29352 74463 41505 87236 69428 05253 81038 06280 5580…

y

X

X*Y

X*Y*Z

Multiplication

Circle Sphere

Thales's theorem

Thales's theorem

Trigonometric Functions

π

Normal distribution

0 1

Is it that, all the underlying mechanisms of nature can be

traced to these fundamental interactions between counting

and right angle which derives from circle?

Or it’s them (or some of them) that set the limits on our Math?

Thank You!