 # Center of Gravity of an L-Shaped Sheet and the Golden Ratio

Initializing live version Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

An L-shaped sheet is constructed by cutting out a square piece from a larger square. The center of gravity (marked as the green point) of the L-shaped sheet shifts as the size of the removed square increases. The center of gravity is outside the L shape if the side of the removed square is greater than the reciprocal of the golden ratio (i.e. ) relative to the side of the larger square.

Contributed by: Sándor Kabai (November 2019)
Open content licensed under CC BY-NC-SA

## Details

In this Demonstration, the L shape is divided into two rectangles in two different ways. The center of gravity is then at the intersection of two lines connecting the centers of each pair of rectangles. A proof is given in .

References

 Wikipedia. "Locating the Center of Mass." (Nov 8, 2019) en.wikipedia.org/wiki/Locating_the_center_of_mass.

 R. Knott. "Two-Dimensional Geometry and the Golden Section or Fascinating Flat Facts about Phi." (Nov 8, 2019) personal.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi2DGeomTrig.html.

 N. Lord, "Balancing and Golden Rectangles," The Mathematical Gazette, 79(486), 1995 pp. 573–574.

## Snapshots   ## Permanent Citation

Sándor Kabai

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send