Scroll to Prove
√2
A length that exists. But can it be measured?
Step I: The Assumption
Assume it is Rational.
If it is rational, it fits the grid. It can be written as a fraction of two integers a and b.
√2 = a⁄b
Step II: The Algebra
Square both sides.
2 = a²⁄b²
a² = 2b²
This means a² is even.
Therefore, a must be even.
Step III: The Fatal Flaw
If a is even, let a = 2k.
(2k)² = 2b²
4k² = 2b²
2k² = b²
Wait. This means b is also even.
Infinite Descent Detected
Irrational.
The grid cannot hold it. It exists outside the ratio of numbers.