One fascinating property of a rectangle inscribed in an octagon is that its side ratio aligns perfectly with the “silver ratio“, or 1+√2. But there’s more to discover! Without doing any calculations, can you prove that the area of this gray rectangle is exactly half of the full octagon’s area? Give it a try!
The “silver ratio” is connected to various mathematical concepts, such as Pell numbers and continued fractions. It serves as the limiting ratio of consecutive Pell numbers, similar to how the golden ratio relates to Fibonacci numbers.
