# The Golden Ratio

Reference > MathematicsThe Golden Ratio -- decimal representation, exact value, algebraic representation, and some history.

The Golden Ratio shows up in nature -- the number of spirals on many plants, the shape of a seashell, and more

The Golden Ratio appears in geometry and trigonometry, in a 72-72-36 triangle.

The Golden Ratio can be written as a continued fraction, as shown with proof on this page.

The Golden Ratio can be written as a continued radical, as shown with proof on this page.

The Golden Ratio is the limit of the ratios of successive terms of a Fibonacci Sequence.

If a Fibonacci Sequence is also a geometric sequence, the ratio of terms is the Golden Ratio.

When you combine The Golden Ratio with some numerology, you get an amusing result: The Mark of the Beast!

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