Prove Pythagoras' theorem using as much technobabble as possible.
To prove the Pythagorean Theorem, we can utilize a mathematical concept known as vector calculus. In this case, we can represent the sides of a right-angled triangle as vectors in a multi-dimensional space.

Let's consider the vectors A and B to represent the sides adjacent and opposite to the right angle, respectively. According to the theorem, the magnitude of the vector C, which represents the hypotenuse, can be expressed as the square root of the sum of the squares of the magnitudes of the vectors A and B. Mathematically, this can be represented as:

|C| = √(|A|^2 + |B|^2)

We can also express this theorem in terms of the dot product of the vectors A and B. The dot product of two vectors can be calculated as the product of the magnitudes of the vectors and the cosine of the angle between them. In this case, as the angle between the vectors A and B is 90 degrees, the cosine of the angle is equal to zero. Hence, the dot product of the vectors A and B becomes:

A.B = |A| * |B| * cos(θ) = 0

From the properties of dot product, we can write the expression for the square of the magnitude of the vector C as:

|C|^2 = |A|^2 + |B|^2

Thus, we can conclude that the Pythagorean Theorem is a fundamental result of vector calculus, which establishes a relationship between the magnitudes of the sides of a right-angled triangle.