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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.
Convolution TheoremsThe convolution theorem states that convolution in time domain corresponds to multiplication in frequency domain and vice versa:Proof of (a):Proof of (b):
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 .