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45-45-90 Triangle

Definition

Defining inequalities

y>=0 and a>=x + y and x>=0

Lamina properties

(0, a) | (0, 0) | (a, 0)

a>0

(data not available)

A = a^2/2

x^_ = (a/3, a/3)

Mechanical properties

J_x invisible comma x = a^4/12

J_y invisible comma y = a^4/12

J_zz = a^4/6

J_x invisible comma y = -a^4/24

r_x = a/sqrt(6)
r_y = a/sqrt(6)

K = a^4 (1/12 - (16 sum_n^∞ coth(1/2 π (2 n - 1))/(2 n - 1)^5)/π^5)

Distance properties

a | a | sqrt(2) a

sqrt(2) a

p = (2 + sqrt(2)) a

r = a - a/sqrt(2)

R = a/sqrt(2)

sqrt(2) a

χ = 1

s^_ = 1/30 a (2 + 4 sqrt(2) + (4 + sqrt(2)) sinh^(-1)(1))

A^_ = a^2/24

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