# Science Quiz / HCHS Math Theorems

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## Can you name the HCHS Math Theorems?

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Every number has a unique prime factorization.
Every even number great than 2 is the sum of two prime numbers.
Relates the lengths of the sides of a triangle to the cosine of one of its angles.
Every positive integer can be written as the sum of the squares of four non-negative integers.
Uses determinants of matrices to solve a 2-variable system of equations.
Any polynomial with real or complex coefficients has at least one root in the complex plane.
Uses derivatives to help evaluate limits involving indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to an expression that
States that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.
If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes will be equal.
The instantaneous slope is equal to the average slope on the interval.
Gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C.
Any real-valued differentiable function that attains equal values at two distinct points must a stationary point between them where the first derivative is zero.
The average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
States that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation.
If equilateral triangles are constructed on the three sides of a given triangle, the centers of the 3 equilateral triangles will themselves form an equilateral triangle.
The indefinite integral is related to its antiderivative, and can be reversed by differentiation.
First order logic is semantically complete. But it is not syntactically complete.
states that if p is a prime number, then for any integer a, the number a^p − a is an integer multiple of p.
the negation of a conjunction is the disjunction of the negations; and the negation of a disjunction is the conjunction of the negations.
states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
a² + b² = c²
If you add up a set of numbers down a direct diagonal of Pascal's Triangle, they will equal the number of the next row in the opposite diagonal direction.
The absolute value of the dot product of two vectors is less than or equal to the product of the magnitudes of the vectors.
The definite integral of a function can be computed by using one of its infinitely-many antiderivatives.
Theorem for generating tessellating irregular hexagons in the plane from an equilateral triangle and a separate point.
It is impossible to separate any power higher than the second into two like powers
Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete.
Regardless of how your data is distributed, if you take the mean of several samples and plot them, the resulting curve will be approximately normal.

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Created Jan 26, 2017
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