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Mollweide's Formulas

Mollweide's formulas relate the side lengths a, b, and c of a triangle to its angles A, B, and C:

(b-c)/a=(sin[1/2(B-C)])/(cos(1/2A))
(1)
(c-a)/b=(sin[1/2(C-A)])/(cos(1/2B))
(2)
(a-b)/c=(sin[1/2(A-B)])/(cos(1/2C)).
(3)

The companion sum identities are called Newton's formulas (Beyer 1987, p. 146), although the sum and difference identities are also grouped together as Mollweide's formula or Mollweide's equation (Karjanto 2011, pp. 70-71).

See also

Newton's Formulas, Triangle, Trigonometry

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References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 146, 1987.Karjanto, N. "Mollweide's Formula in Teaching Trigonometry." Teaching Math. Appl. 30, 70-74, 2011. https://doi.org/10.1093/teamat/hrr008.

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Mollweide's Formulas

Cite this as:

Weisstein, Eric W. "Mollweide's Formulas." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MollweidesFormulas.html

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