## Cynthia Lanius

## Golden Ratio Algebra

Golden Ratio 1.61803

Golden Ratio Table of ContentsIntroduction Find golden rectangles. Build golden rectangles. Confirm the ratio using algebra. ## We used this property when we built the rectangle, and now we will use it to confirm the value of the golden ratio.

One property of golden rectangles is that their

length (length + width) ------ = ---------------- width lengthWhen we cross multiply the above proportion, we get

l Enter this into a calculator, and you'll see the approximation of the golden ratio -^{2}= lw + w^{2}orl

^{2}- lw - w^{2}= 0.Solving the equation gives us

l = w(1 + sqrt5) ------------ 2Divide both sides by w:l = (1 + sqrt5) --- --------- w 21.61803398874989484820 There you have it, the derivation of the Golden Ratio.

Golden Ratio Table of ContentsIntroduction Find golden rectangles. Build golden rectangles. Confirm the ratio using algebra. Email any comments to lanius@math.rice.edu Geometry Online Index

## Copyright 1998-2008 Cynthia Lanius

URL http://math.rice.edu/~lanius/Geom/algebra.html