I encountered Mollweide's formula and I search the net for the proof.. I got this link http://planetmath.org/encyclopedia/ProofOfMollweidesEquations.html . I studied the proof and it requires a lot of trigonometric identities. Can we have another means in proving this identity? A better approach? thanks a lot in advance..:)

By the way the Mollweide's formula is:

Given any triangle with $a,\ b,\ c, \ \alpha ,\ \beta, \ \gamma $.$$\frac{a+b}{c}= \frac{\cos (\frac{\alpha - \beta}{2})}{\sin (\frac{\gamma}{2})}$$ and $$\frac{a-b}{c}= \frac{\sin (\frac{\alpha - \beta}{2})}{\cos(\frac{\gamma}{2})}$$

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    For those like me who did not know about them, here is a link to Mollweide's formula. – lhf Mar 5 '12 at 12:32
  • @lhf, thanks for the link ..:).. I forgot to put the formula, So, I edited it. thanks anyway. – Keneth Adrian Mar 5 '12 at 12:35
up vote 7 down vote accepted

Mollweide's formula: proof without words

Screenshot from http://cartography.tuwien.ac.at/content07/index.php?download=Lapaine_Mollweide_draft_paper.pdf

Proof attributed to H. Arthur De Kleine, "Proof Without Words: Mollweide's Equation", Mathematics Magazine, volume 61, number 5, page 281, December, 1988.

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