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Circle Area = 50.2654824574

 

Shaded Fraction = 1 / 9

Roots: ( 2 ; √ 2 ) & ( √ 2 ; 2 )

Min Shaded Fraction = 4 / 13

Graph showing Shaded Area

Proof: a / b = 2

Shaded Fraction = 13 / 16

Blue / Orange = 27 / 28

Angle JKL = X = 60°

Ratio of Red / Green = 4 / 5

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Radius R = 0.343145750508

R = 1 / 6 = 0.166666666667

White Area = 6

Radius R = 0.568158087681

Shaded Fraction = 6 / 17

Radiuses R₁, R₂, R₃, R₄ = ?

Radius R = 6.22341038101

Shaded Fraction = 37 / 192

Green / Orange = 3 / 2 = 1.5

sin α + sin 3α = 32 / 27

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Blue Area = 8 / 5 = 1.6

△ EGH / △ ABC = 8 / 35

Ratio of Green / Orange = 1

X = 1.73205080757 = √ 3

180° - 60° - 40° - 40° = 40°

Angle BGF = X = 54°

Side s = 1.0973423128

Angle DQP = X = 75°

XY = Shaded Area

Red Fraction = 1 /4 = 0.25

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Green / Mauve = 2

 

Green / Mauve = 4 / 5 = 0.8

Alpha = Beta = 60°

With Circle: Alpha = Beta = 60°

cos α = 0.414213562373

Green = ( π ⋅ 5 / 8 - 1 ) ⋅ S

BAF = ADE = DCH = CBG = 15°

Mauve = 9.79795897113

ABD = X = 45°

Angle CHD = X = 18°

Angle BFH = X = 36°

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Line Segment HK = b - a

c / ( a + b ) = 1 ⇒ a + b = c

Radius R = 0.686291501015

Angle BEH = X = 15°

Number of Segments = 15

Ratio of X / Y = 1 / 3

EF = 1.41421356237

Shaded Fraction = 1 / 2 = 0.5

Orange = 1.16861669869

ELABORATED / ANIMATED

Line Segment AH = X = 4