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a / b = 1.41421356237

Ratio = 0.214359353945

Angle AFE = 76°

ECF = 45° ⇒ Blue Area = 6

ECF = 45° ⇒ Blue = 6 ( Elaborated )

Dodecagon. Find a, b, c, d

Mauve / Total = 3 / 5

Red Area / Orange Area = 1

EF = √ 2 = 1.41421356237

Archimedes' Twin Circles

Area ABC = 40.2265191075

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Second Coordinate p = 0.360034982809

Second Coordinate s = 10.8096575357

Radius R = 0.252122461732

Area of Blue Square = 10

Side s = 2.64575131106

Line Segment HP = X = 13

AD = X = 6.40312423743

Angle CEF = X = 66°

Side s = 14.6556098406

X / Y = 1.61803398875

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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

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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.

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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