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Reuleaux Triangle

Definition

Defining inequalities

(x - a/2)^2 + (a/(2 sqrt(3)) + y)^2<=a^2 and (y - a/sqrt(3))^2 + x^2<=a^2 and (a/2 + x)^2 + (a/(2 sqrt(3)) + y)^2<=a^2

Alternate name

Lamina properties

a>0

A = 1/2 (π - sqrt(3)) a^2

x^_ = (0, 0)

Mechanical properties

J_x invisible comma x = 1/48 (10 π - 17 sqrt(3)) a^4

J_y invisible comma y = 1/48 (10 π - 17 sqrt(3)) a^4

J_zz = 1/24 (10 π - 17 sqrt(3)) a^4

J_x invisible comma y = 0

r_x = 1/2 sqrt(5/3 + 7/(6 - 2 sqrt(3) π)) a
r_y = 1/2 sqrt(5/3 + 7/(6 - 2 sqrt(3) π)) a

Distance properties

p = π a

r = (1 - 1/sqrt(3)) a

R = a/sqrt(3)

χ = 1

Classes