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Fibonacci is most known for his sequence. It is 1, 1, 2, 3, 5, 8, 13,... You get a term by adding the two previous terms.
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Kepler was well known for his laws that dealt with the orbit of planets around the sun.
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Newton is one of the founding fathers of calculus. He is also famous for developing a general formula for expanding a binomial.
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Leibniz is the other founder of calculus, Newton being the other. While Newton often receives most credit for calculus, it is the notation of Leibniz that is still used widely to this day.
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Euler had large contributions in the field of analysis by proving the power series expansion of the natural exponential function. He also is well-known for his formula that explains the relationship between complex numbers and trigonometric functions.
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Gauss is one of the most influential people in the world of mathematics. A common fact about Gauss is that he was so bored in school that his teacher told him to add up the numbers between 1 and 100. He did this very quickly by finding a pattern and developing a formula.
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August Mobius is most known for his Mobius strip, an object with only one surface.