Geometric Perspective
Consider completing the square for the equation
Since x2 represents the area of a square with side of length x, and bx represents the area of a rectangle with sides b and x, the process of completing the square can be viewed as visual manipulation of rectangles.
Simple attempts to combine the x2 and the bx rectangles into a larger square result in a missing corner. The term (b/2)2 added to each side of the above equation is precisely the area of the missing corner, whence derives the terminology "completing the square".
Read more about this topic: Completing The Square
Famous quotes containing the words geometric and/or perspective:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
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The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“Egoism is the law of perspective as it applies to feelings, according to which what is closest to us appears to be large and weighty, while size and weight decrease with our distance from things.”
—Friedrich Nietzsche (1844–1900)