Square Inside of Circle, Square Outside of Circle: Perimeter

The perimeter of the inside square is 1/√2 or (1 ÷ √2) the perimeter of the outside square, using the diameter (d).

OR
The perimeter of the inside square is (√2)/2 or (√2 ÷ 2) the perimeter of the outside square, using the radius (r).

1/√2 or (1 ÷ √2)  =  (√2)/2 or (√2 ÷ 2) = 0.707.

Square Inside of Circle, Square Outside of Circle: Area

The area of the inside square is half (1/2) the area of the outside square.

Calculating the area of a circle using the Pythagorean theorem

 Calculating the area of a circle using the Pythagorean theorem.

Calculating the circumference of a circle using Pi (π) versus using triangles (trigonometry)

Calculating the circumference of a circle:
1. Using Pi (π), versus

2. Using Triangles (Trigonometry)

Prime Numbers Pattern

Prime numbers follow a pattern, making it possible to predict them.
Excluded from the pattern, are the multiples of the primes.

This is presented in a "family of five", to make it easier to see the pattern.

5 people have 20 unique impressions

5 people have 20 unique impressions:
Amy, Eva, Joy, Kim, Pam:
1. Amy + Eva (Amy of Eva, Eva of Amy) = 2.
2. Amy + Joy = 2.
3. Amy + Kim = 2.
4. Amy + Pam = 2.
5. Eva + Joy = 2.
6. Eva + Kim = 2.
7. Eva + Pam = 2.
8. Joy + Kim = 2.
9. Joy + Pam = 2.
10. Kim + Pam = 2.
Total = 20

5 people have 10 unique connections

5 people have 10 unique connections:

Amy, Eva, Joy, Kim, Pam:

1. Amy + Eva.

2. Amy + Joy.

3. Amy + Kim.

4. Amy + Pam.

5. Eva + Joy.

6. Eva + Kim.

7. Eva + Pam.

8. Joy + Kim.

9. Joy + Pam.

10. Kim + Pam.