A Golden Ratio Infinite Series Dissection (visual proof)

Описание: This is animated visual proof demonstrating the sum of the infinite series of the reciprocals of even powers of the golden ratio is the golden ratio. We also get a related fact showing the sum of the reciprocals of the reciprocals of the odd powers of the golden ratio. This dissection proof utilizes the so-called "golden gnomon" and the "golden triangle".

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To see the proof that the golden triangle has the dimensions stated, see this video:    • Golden Ratio is Irrational from a Regular ...  

For more infinite series dissections, check out this playlist:
   • Infinite Series  

Here is a longer form video with lots of infinite geometric sums:    • Beautiful Geometry behind Geometric Series...  

This animation is based on a visual proof by Steven Edwards from the March 2014 issue of The College Mathematics Journal (https://doi.org/10.4169/college.math.... - page 120).

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