Golden+Ratios

Paul Han - Golden Ratio in Monalisa
 * the golden ratio = 1.61803399 - JN**
 * Golden Ratio represented by Greek letter phi- Sunil **
 * Golden Ratio was used in ancient greek buildings-CJ **

The figure above is representing a golden rectangle. Square A is proportionate to rectangle B. Both figures (A and B) are proportionate to the whole rectangle. The figure relates to the chapter because you can find examples of golden rectangles in not only diagrams but everyday life. - Douglas Apple __ []- zack mckelvie __

__ The golden rectangle must be able to split into a square and a similar rectangle of the original rectangle- __
v This figure below represents a golden rectangle, with many golden rectangles repeating inside of it. It is very important to see how the golden rectangle can be repeated and I find it very interesting. Figure ABEF is a square and figure FCDE is proportionate to figure ABCD. -Andrew Chimes ABOVE ^^ Each side of the colored squares are proportionate to the sides of all of the other golden squares-CJ

The flower can be an example of the golden ratio because the designs are proportionate to the designs on the flower. - Douglas Apple

<- Grey golden rectangle- can be split into a square and a rectangle similar to the original shape- Zack McKelvie = Golden Pentagon -Jen Nam=

Golden Triangle: If there is an isosceles triangle that has the two base angles of 72 degrees and one of its base angle is bisected it will form two triangles where one of the triangles is similar to the original triangle. -Alex Pham

examples of golden ratio. The Mona Lisa's body is an example of golden rectangle with the body in the square and her head in the rectangle that is similar to the original rectangle. The greek buildings were built off of the ideas of the golden rectangle making each part of the building similar to the original rectangle.-CJ Jen Nam Douglas Apple

**- Sunil** These are all examples of the golden ratio. The golden rectangle is when you split the rectangle into a square or rectangle and it is similar to the original. The picture that has the candy canes is an example of one because when you split the full rectangle into another piece, they are similar to each other. This is the same for the parthenon as well. In the Mona lisa picture, when you divide it into more triangles, they are similar to the larger triangle. - Matt H



The Golden Ratio was actually found in the great pyramid of giza which came 4,600 years ago and way before the greeks. The golden ratio is the ratio 1.61803 39887 49894 84820 and makes infinite rectangles of the same proportion. - Andrew Himes

Golden ratio conjugate
The negative root of the quadratic equation for **φ** (the "conjugate root") is The absolute value of this quantity (≈ 0.618) corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, //b/a//), and is sometimes referred to as the //golden ratio conjugate//.[|[][|10][|]] It is denoted here by the capital Phi (**Φ**): Alternatively, **Φ** can be expressed as This illustrates the unique property of the golden ratio among positive numbers, that or its inverse: Although this looks very confusing, it is showing how to get the what the golden ratio is equal to. The golden ratio equals 0.6180339887... Here are a few scenarios if you are looking to find how to get the golden ratio and what it equals. It includes a fraction along with adding or subtracting the greek letter phi. -Douglas Apple

Divide any of the Fibonacci numbers by the next higher number [and] the sequence of ratios will converge to 0.618. Dividing a number by its previous number will converge to 1.618. The Greeks knew this proportion and called it the ‘Golden Mean’. -CJ

This ear is an example of the Golden Ratio because it is based off of the Golden Rectangle. Each part of the ear is proportionate to the whole ear. -CJ



If you have a rectangle whose sides are related by phi, that rectangle is said to be a Golden Rectangle. To make one you start off wilth 1by 1 and continuby 'swinging' the long side around one of its ends to create a new long side, then that new rectangle is also Golden Rectangle -Sunil

The Golden Ratio has many examples such as in nature, painting and in yourself. Here are some examples:-Sunil

-Your forearm is approximately 1.618 times as long as your hand.

-Peoplesometimes haveh mouths 1.618 times as wide as their noses. -Distance between your pupils is about 1.618 times as wide as their mouths. -The leaves and stems of some trees are arranged at 137.5 degrees from each other. That angle lets the sun shine on the greatest number of leaves. When you draw that angle inside a circle, you get two pieces. Divide 137.5° into 222.5° and you get 1.618

-In the Mona Lisa the womens face is 1.618 time as long as it is wide and this is also the same with the Parthenon ﻿ - IF you inscribe a regluar decaon into a circle, the ratio of the side of the decagon to the radius of the circle is 1.618 

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