The 2.1.2 sum-of-squares [SOS] equation $$a^2=b^2+c^2$$ can be thought of in the [regular XY] plane as a right-angled triangle.

Question: Is there an analogous interpretation for every SOS equation?

For example, does the 2.1.3 SOS equation $$a^2=b^2+c^2+d^2$$ have an interpretation in plane geometry?

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    $\begingroup$ Just put a few right-angled triangles, the hypotenuse of one being the cathetus of the next. $\endgroup$ – user551819 Apr 27 '18 at 20:10
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    $\begingroup$ "Cathetus" - I've learned something today! $\endgroup$ – J.G. Apr 27 '18 at 20:14
  • $\begingroup$ @user170231 The question asked for plane geometry. $\endgroup$ – J.G. Apr 27 '18 at 20:15
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    $\begingroup$ @KierenMacMillan Every single time that I have to spell that word I have to Google and end up finding the spelling in this Wikipedia page. $\endgroup$ – user551819 Apr 27 '18 at 20:27
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    $\begingroup$ @IshanSingh: 2.1.3 refers to the exponent (2) and the number of summands on each side of the equation (1 on the LHS, 3 on the RHS). This is a notational convention going back to at least the 1950s. $\endgroup$ – Kieren MacMillan May 20 '18 at 14:22

$$ a^2=b^2+c^2+d^2 \quad\hbox{and}\quad p^2+q^2+r^2=s^2+t^2. $$

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  • $\begingroup$ This is amazing. Thank you! $\endgroup$ – Kieren MacMillan Apr 27 '18 at 21:50

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