Convolution Theorems
The convolution theorem states that convolution in time domain corresponds to multiplication in frequency domain and vice versa:
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Fundamental theorem of arithmetic :- Every composite number can be expressed (factorized) as a product of primes, and this factorization is unique . apart from the other in which factors occur.
states that the external effect of force are independent of the point of application of the force along its line of action.
The empirical rule can only be used for a normal distribution, so I will assume you are referring to a normal distribution. Chebyshev's theorem can be used for any distribution. The empirical rule is more accurate than Chebyshev's theorem for a normal distribution. For 2 standard deviations (sd) from the mean, the empirical rule says 95% of the data are within that, and Chebyshev's theorem says 1 - 1/2^2 = 1 - 1/4 = 3/4 or 75% of the data are within that. From the standard normal distribution chart, the answer for 2 sd from the mean is 95.44% So, as you can see the empirical rule is more accurate.
Pythagoras most famous proof is the pythagorean proof . It states that in a right angled triangle , the square of hypoteneus ( the longest side of the triangle ) is equal to the sum of squares of the other two sides .