# Category:Golden Mean

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This category contains results about **Golden Mean**.

Definitions specific to this category can be found in Definitions/Golden Mean.

Let a line segment $AB$ be divided at $C$ such that:

- $AB : AC = AC : BC$

Then the **golden mean** $\phi$ is defined as:

- $\phi := \dfrac {AB} {AC}$

## Subcategories

This category has the following 10 subcategories, out of 10 total.

## Pages in category "Golden Mean"

The following 47 pages are in this category, out of 47 total.

### A

- Algebraic Number/Examples/Golden Mean
- Approximation to Golden Rectangle using Fibonacci Squares
- Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio
- Area of Square on Lesser Segment of Straight Line cut in Extreme and Mean Ratio
- Area of Squares on Whole and Lesser Segment of Straight Line cut in Extreme and Mean Ratio

### C

- Closed Form for Lucas Numbers
- Closed Form of One Minus Golden Mean
- Construction of Golden Section
- Continued Fraction Expansion of Golden Mean
- Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio
- Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio/Lemma
- Cosine of 36 Degrees

### F

- Fibonacci Number by Golden Mean plus Fibonacci Number of Index One Less
- Fibonacci Number by One Minus Golden Mean plus Fibonacci Number of Index One Less
- Fibonacci Number greater than Golden Section to Power less Two
- Fibonacci Number less than Golden Section to Power less One
- Fibonacci Number n+1 Minus Golden Mean by Fibonacci Number n
- Fibonacci Number of Even Index by Golden Mean Modulo 1
- Fibonacci Number of Odd Index by Golden Mean Modulo 1

### G

### R

### S

- Segments of Rational Straight Line cut in Extreme and Mean Ratio are Apotome
- Sequence of Golden Rectangles
- Sequence of Golden Rectangles/Equiangular Spiral
- Sequence of Powers of Golden Mean
- Sine of 36 Degrees
- Sine of Multiple of Pi by 2 plus i by Natural Logarithm of Golden Mean
- Square of Golden Mean equals One plus Golden Mean
- Square of Golden Mean equals One plus Golden Mean/Decimal Expansion
- Straight Line cut in Extreme and Mean Ratio plus its Greater Segment
- Straight Lines Subtending Two Consecutive Angles in Regular Pentagon cut in Extreme and Mean Ratio
- Sum of Alternating Sign Reciprocals of Sequence of Pairs of Consecutive Fibonacci Numbers is Reciprocal of Golden Mean Squared
- Sum of Consecutive Odd Index Fibonacci Numbers
- Sum of Reciprocals of Sequence of Pairs of Even Index Consecutive Fibonacci Numbers is Reciprocal of Golden Mean Squared
- Sum of Reciprocals of Sequence of Pairs of Odd Index Consecutive Fibonacci Numbers is Reciprocal of Golden Mean