Pythagorases Theorm
January 24th, 2008
The Theorem
“The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides in a right angled triangle”
or mathematically
c2 = b2 + a2
This is very useful for allot of applications.
Applications of the theorem
There are many applications of Pythagoras besides simple triangles
eg)The difference between colors. Yes using pythag we can measure the “difference” between to colors as a number. This is how
- take you first and second color as a rgb number eg) red = 256 ,0,0 and a light shade of blue is 30, 100, 256.
- square the difference between the values for red, green and blue
- then find the square root of the sum of these values
Why does this work, because the hypotenuse of one triangle can be used as the base of another, and this triangle can be tilted by 90 degrees into the z plane the theorem can work in 3D 
. We can then change the x,y and z axis to values for r,g,b. As pythag works in 3D we can calculate the distance between to colors(which are points in the rgb axis)
Comments Left
dum ass
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Using 20 as the hypotenuse what are the most possible values that can be used for a and b in the formula. Thes are hole numbers.
What would this formula be to establish this?
Apologize, on expression mathematically above c^2 = a^2 + b^2 isn’t it?
and not a^2 = b^2 + c^2.
thanks for telling me
By the most possible values do you mean that the sum of a and b is greatest, or the largest value of a with the corresponding b value. I’m guessing the largest values of the sum of a and b is 28 where a = 16 and b = 12 as this makes a “3,4,5″ triangle which I believe to be the Pythagorean triangle where a-b is smallest as these triangles usually have a difference of 1 between their largest and middle sides. Hopefully that answers your question though it doesn’t actually prove anything – just a suggestion.