## Squaring the Circle

### In 1882, the task was proven to be impossible, as a consequence of the Lindemann-Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if π were transcendental, but π was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π. ### The synodic period is the time between two successive new moons or full moons. This is called a synodic or lunar month with a long-term average duration of 29.531 days. ### Squaring a given circle according to practically equal areas results in a square with an area which is 27.32% larger than the area of the square belonging to equal  perimeter/circumference. The 35th layer represents the Moon

• ### The average length of a human pregnancy is 10 sidereal months is 273 days • ### It takes the Sun an average of 27.3 days to rotate around its own axis 