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
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Introduction This experiment focuses on two concepts. These concepts are Proportionality and Superposition theorems. Proportionality is a way to relate two quantities together. This means that when more input is supplied‚ you get more output which is proportional to the input. The Proportionality Theorem states that the response in a circuit is proportional to the source acting in the circuit. This is also known as Linearity. The proportionality constant (K) relates the input voltage to the
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display the temperature at that depth in degrees Celsius and Fahrenheit. The relevant formulas are: Celsius = 10 x (depth) + 20 (Celsius temperature at depth in km) Farhrenheit = 1.8 x (Celsius) + 32 8. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. For example‚ if two sides of a right triangle have lengths 3 and 4‚ then the hypotenuse must have a length of 5. The integers 3‚ 4‚ and 5
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EXPERIMENT NO. 10 Thevenin’s Theorem Objectives: 1. To verify the Thevenin’s theorem through an experiment. 2. To find the Thevenin’s resistance RTH by various methods and compare values. Equipment: Resistors‚ DMM‚ breadboard‚ DC power supply‚ and connecting wires. Theory: Thevenin theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in series with a resistance RTH where * VTH is the open-circuit voltage at
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Bayes’ theorem describes the relationships that exist within an array of simple and conditional probabilities. For example: Suppose there is a certain disease randomly found in one-half of one percent (.005) of the general population. A certain clinical blood test is 99 percent (.99) effective in detecting the presence of this disease; that is‚ it will yield an accurate positive result in 99 percent of the cases where the disease is actually present. But it also yields false-positive results in 5
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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
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central The Central Limit Theorem A long standing problem of probability theory has been to find necessary and sufficient conditions for approximation of laws of sums of random variables. Then came Chebysheve‚ Liapounov and Markov and they came up with the central limit theorem. The central limit theorem allows you to measure the variability in your sample results by taking only one sample and it gives a pretty nice way to calculate the probabilities for the total ‚ the average and the proportion
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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
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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
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How We Use the Pythagorean Theorem in Everyday Life First‚ let’s discuss the inventor of the theorem before how we use it. Pythagoras of Samos is a very odd fellow but is very well known despite not have written anything in his lifetime so what we know about him comes from Historians and Philosophers. Though we know he was a Greek philosopher and mathematician mainly known for the Pythagorean Theorem that we all learned in 6th grade. (a2 + b2 = c2). His theorem states that that the square of
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