Top 10.271

R₂ of Semicircle = 1 / 4

R in Terms of Side s

Green = 1.00736221792

Ratio of a / b = 1.61803398875 = ϕ

Line Segment BC = X = 24

BF = X = 0.57735026919

X = 2 ( Regression 1 )

X = 2 ( Regression 2 )

X = 2 ( Without Regression )

Area of Blue Triangle = 18

Orange = 2572.96438329

Minor Radius R₁ = 0.261203874964

Top 10.270

Angle ABC = X = 162°

Paper folding

| GJ | = h ⇒ h / w = √ ( ϕ )

Proof: Ratio = 1

Line Segment BD = X = 3

Radius R = 4

White Area = 4.69875190279

Intersection between 2 lines

Ratio = 81 / 16 = 5.0625

Green Area in Terms of R

S of Square / S of Hexagon.

Top 10.269

Shaded Area = 8

Yellow = 392.699081699

Perimeter of Orange Region

Shaded Fraction = 3 / 14

Green Area = 20

Blue = 1 ⇒ Green = 4

Perimeter of △ BDE = 30

Shaded Fraction = 1 / 3

X = AD = 2, Y = BD = 1.

Circle Area = 18.8577911987

Top 10.268

Circles in Resizable Triangle

Angle AGM = 45°

Line Segment GM = X = 12

Proof: Radius R = 40

Radius R = 40 ( NEW )

Angle BCD = X = 30°

Red Area = 54

Shaded Fraction = 3 / 64

Calculation of X = | AE |

Total = 24 ⇒ Orange = 7

Shaded = 41.5938984451

Top 10.267

Radius R = 5.83095189485

Red Arc / ( Blue Arc + Orange Arc ) = 3 / 4

Two Circles and a Square

3 Semicircles, 2 Circles

1 Circle, 3 Semicircles (simplified)

Ellipse Segment Fraction: 0.601987296981

BAC = 63.4349488229°

Angle DCE = X = 15°

Ratio of a : b = 3

Max ( Red Area ) = 1