Golden Mean: Post 2

Golden Mean, Golden Rectangle, Golden Spiral: 

Golden Rectangle

Original Photograph by Kaitlin M.

The following description was written by Angela M: "Our IDs as a whole resemble a golden rectangle. You can see that the area with the red background creates another golden rectangle and the rest is cut off into a square."

The measurements are as follows: 

ID card: L - 8.5 cm, W - 5.4 cm

Red rectangle: L - 5.4 cm, 3 cm

It can be argued that the ID card itself is a golden ratio. 8.5 / 5.4 = 1.574, which is close enough to phi (1.618) to convince one that a golden ratio was the goal. The red rectangle, however, does not have this same justification. Not only is it way too large for it to be considered a golden rectangle itself, but the part at which it was cut off is also not close enough to phi to justify calling it a golden mean. The Wheaton portion of the ID has a length of 5.5 cm, while the red rectangle has a width of 3. 5.5 / 3 = 1.83, which is way too large for phi. 

It was a rather clever choice, and we were initially convinced that it was divided according to the principles of the golden mean. While it's sad that it doesn't quite add up, it definitely got us to think a lot more about these everyday objects we tend to take for granted.

Original post from the Math 125 blog can be found here.