3
$\begingroup$

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?

$\endgroup$
  • 3
    $\begingroup$ 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
  • 1
    $\begingroup$ "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
  • 1
    $\begingroup$ @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
  • 1
    $\begingroup$ @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
11
$\begingroup$

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

enter image description here

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.