Fermat’s Last Theorem Fermat’s Last Theorem states that no three positive integers‚ for example (x‚y‚z)‚ can satisfy the equation x^n+y^n=z^n if the integer value of n is greater than 2. Fermat’s Last Theorem is an example a Diophantine
Premium
The Pythagorean theorem (A^2 + B^2 = C^2) has been impacting all types of people and careers since it was first realized during Ancient Greece times. It is one of the most widely recognized theorems in the mathematics community‚ and used much more than the average person knows: whether you need need to know the dimensions of a bag or you need find the distance from location to another‚ the Pythagorean theorem can be used. Everyone who was taught this theorem in their first year of algebra continues
Premium Mathematics Scientific method Isaac Newton
CENTRAL LIMIT THEOREM There are many situations in business where populations are distributed normally; however‚ this is not always the case. Some examples of distributions that aren’t normal are incomes in a region that are skewed to one side and if you need to are looking at people’s ages but need to break them down to for men and women. We need a way to look at the frequency distributions of these examples. We can find them by using the Central Limit Theorem. The Central Limit Theorem states that
Premium Standard deviation Normal distribution Sample size
mathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics‚ such as Fermat’s Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle‚ the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. A particularly simple one is the scaling relationship
Premium Pythagorean theorem Mathematics Triangle
4.14 TRIANGLES Triangles are three-sided shapes that lie in one plane. Triangles are a type of polygons. The sum of all the angles in any triangle is 180º. Triangles can be classified according to the size of its angles. Some examples are : Acute Triangles An acute triangle is a triangle whose angles are all acute (i.e. less than 90°). In the acute triangle shown below‚ a‚ b and c are all acute angles. Sample Problem 1: A triangle has angles 46º‚ 63º and 71º. What type of triangle is this? Answer:
Premium Triangle Pythagorean theorem Triangles
The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal‚ Neeraj Kayal‚ and Nitin Saxena‚ computer scientists at the Indian Institute of Technology Kanpur‚ on August 6‚ 2002‚ in a paper titled "PRIMES is in P".[1] The authors received many accolades‚ including the 2006 Gödel Prize and the 2006 Fulkerson Prize‚ for this work. The algorithm determines whether a number
Premium Prime number
The world is divided into two sets: the W.E.I.R.D‚ (Western‚ Educated‚ Industrialized‚ Rich and Developed) and the non-W.E.I.R.D. world. The W.E.I.R.D world includes North America‚ Europe and most of Latin America‚ while East Asia‚ Pacific‚ South Central Asia‚ MENA‚ and sub-saharan Africa make up the non-W.E.I.R.D world. Obviously‚ there are many major differences between these two sets of regions; however‚ in my opinion‚ the geography and development‚ economics‚ and politics demonstrate the differences
Premium United States Europe European Union
Pythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I ’ll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion‚ a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears
Premium Pythagorean theorem Triangle Mathematics
Gauss Markov Theorem In the mode [pic]is such that the following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify
Premium Function Variance Estimator
Chebyshev’s Theorem and The Empirical Rule Suppose we ask 1000 people what their age is. If this is a representative sample then there will be very few people of 1-2 years old just as there will not be many 95 year olds. Most will have an age somewhere in their 30’s or 40’s. A list of the number of people of a certain age may look like this: |Age |Number of people | |0 |1 | |1 |2 | |2 |3
Premium Standard deviation Normal distribution Arithmetic mean