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Subject: "Pythagorean theorem and determinants"     Previous Topic | Next Topic
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gaespes
Member since Feb-1-11
Mar-22-11, 11:30 AM (EST)
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"Pythagorean theorem and determinants"
 
   The Pythagorean theorem as an application of the determinant properties in the plane:

https://w3.romascuola.net/gspes/unitary.html

gaespes


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gaespes
Member since Feb-1-11
Apr-02-11, 10:07 PM (EST)
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1. "RE: Pythagorean theorem and determinants"
In response to message #0
 
   by expressing geometrically the fact that (in the complex plane):

det(a,a*i)=det(ax+ay*i,-ay+ax*i)=det(ax,ax*i)+det(ay*i,-ay)=ax≤det(1,i)-ay≤det(i,1)=ax≤+ay≤

one gets the following equiestentional transformation of parallelograms:

(move c horizontally in the following applet)

w3.romascuola.net/gspes/pug.htm?c=-3.01-2i&a=1+2i&t=1000&f=(floor(cx)<=-4)(ax*t+ax(floor(200t)=200t)i-ax*i)+(floor(cx)=-3)(ax*t+ax(floor(200t)=200t)i)+(floor(cx)=-2)(a*t+ax(floor(200t)=200t)i)+(floor(cx)>=-1)(a*t+(floor(200t)=200t)ax^2(-ay+ax*i)/(ax^2+ay^2))&g=(floor(cx)<=0)(ay*t+ay(floor(200t)=200t)i+ax)+(floor(cx)=1)(ay*t+ay(floor(200t)=200t)i+ax*i-ay)+(floor(cx)=2)(a*t-(floor(200t)=200t)ay+ax*i)+(floor(cx)>=3)(a*t+(floor(200t)=200t)(a*i-ax^2(-ay+ax*i)/(ax^2+ay^2))+ax^2(-ay+ax*i)/(ax^2+ay^2))&h=(floor(7t)=1)a+(floor(7t)=2)ax+(floor(7t)=4)a+(floor(7t)=5)a(1+i)+i(floor(7t)=6)a

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gaespes
Member since Feb-1-11
Apr-06-11, 11:23 AM (EST)
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2. "RE: Pythagorean theorem and determinants"
In response to message #1
 
   .. which, in the substance, is
https://www.cut-the-knot.org/pythagoras/index.shtml#1

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