# Does every sum-of-squares equation have a plane geometric interpretation?

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?

• Just put a few right-angled triangles, the hypotenuse of one being the cathetus of the next. – user551819 Apr 27 '18 at 20:10
• "Cathetus" - I've learned something today! – J.G. Apr 27 '18 at 20:14
• @user170231 The question asked for plane geometry. – J.G. Apr 27 '18 at 20:15
• @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. – user551819 Apr 27 '18 at 20:27
• @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. – Kieren MacMillan May 20 '18 at 14:22

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