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bDistance

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Ivan Pavlov edited this page May 2, 2022 · 1 revision

bDistance[p,q]

Gives the distance between p, q, which are defined in barycentrics. For example, let's calculate the distance between circumcenter and incenter:

OI = bDistance[KimberlingCenterB[1], KimberlingCenterB[3]] // Simplify

result

SymmetricReduction[a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2), {a, b, c}]
{9 a b c + (a + b + c)^3 - 4 (a + b + c) (a b + a c + b c), 0}

SymmetricReduction[a^4 + (b^2 - c^2)^2 - 2 a^2 (b^2 + c^2), {a, b, c}]
{8 a b c (a + b + c) + (a + b + c)^4 - 4 (a + b + c)^2 (a b + a c + b c), 0}

Hence:

result

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