Section 1
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Area of parallelogram
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Cards (75)
Section 1
(50 cards)
Area of parallelogram
Logarithms
Dot Product with vectors
Volume of a prism
Area of rhombi
linear
A polynomial with degree 1, like 3x,
Andrew Wiles
(1953-present, British) is best known for proving the Taniyama-Shimura conjecture that all rational semi-stable elliptic curves are modular forms. When combined with work already done by other mathematicians, this immediately implied Fermat's last theorem (see above).
Area of triangle
1/2 (base)(height)
Complex number
i = square root of -1
Angle between two vectors
domain
the set of possible input values for a function
Area of trapezoid
Archimedes
(287-212 BC, Syracusan Greek) is best known for his "eureka" moment, in which he realized he could use density considerations to determine the purity of a gold crown; nonetheless, he was the preeminent mathematician of ancient Greece. He found the ratios between the surface areas and volumes of a sphere and a circumscribed cylinder, accurately estimated pi, and developed a calculus-like technique to find the area of a circle, his method of exhaustion.
Polynomials
are functions made of terms added together, in which each term is a number times a product of variables raised to nonnegative-integer powers. For instance, 3x2y and -πx7y2z3 are each terms, so 3x2y - πx7y2z3 is a polynomial. (Individual terms are also considered polynomials.) Much of math is concerned with polynomials involving only one variable, such as -x3 + 2x2.
William Rowan Hamilton
(1805-1865, Irish) is known for a four-dimensional extension of complex numbers, with six square roots of -1 (±i, ±j, and ±k), called the quaternions.
binomial
a polynomial with two terms
Pythagorean triples
Sets of small integers that satisfy the equation of the Pythagorean theorem, a^2 + b^2 = c^2, and could therefore be the side lengths of a right triangle. The simplest ones are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, and {8, 15, 17}.
monomial
a polynomial with one term, like 2x or -12x2
Euclid
(c. 300 BC, Alexandrian Greek) is principally known for the Elements, a textbook on geometry and number theory, that has been used for over 2,000 years and which grounds essentially all of what is taught in modern high school geometry classes. The Elements includes five postulates that describe what is now called [blank] space (the usual geometric space we work in); the fifth postulate — also called the parallel postulate — can be broken to create spherical and hyperbolic geometries, which are collectively called non-[blank] geometries. The Elements also includes a proof that there are infinitely many prime numbers.
Volume of a sphere
4/3 x pi x r^3
Volume of a pyramid
Volume of a cylinder
Permutations
EX: Suppose we want to find the number of ways to arrange the three letters in the word CAT in different two-letter groups where CA is different from AC and there are no repeated letters. - is known as 3_P_2, which is 3!/(3-2)!
Surface area of a parallelepiped
2ab+2bc+2ac
Isaac Newton
(1643-1727, English) The work of [blank] in pure math includes generalizing the binomial theorem to non-integer exponents, doing the first rigorous manipulation with power series, and creating [blank]'s method for finding roots of differentiable functions. He is best known, however, for a lengthy feud between British and Continental mathematicians over whether he or Gottfried Leibniz invented calculus (whose differential aspect [blank] called the method of fluxions). It is now generally accepted that they both did, independently.
Surface area of a cylinder
Pierre de Fermat
(1601-1665, French) is remembered for his contributions to number theory including his little theorem, which states that if p is a prime number and a is any number at all, then ap - a will be divisible by p. He studied [blank] primes, which are prime numbers that can be written as 22n + +1 for some integer n, but is probably most famous for his "last theorem," which he wrote in the margin of Arithmetica by the ancient Greek mathematician Diophantus with a note that "I have discovered a marvelous proof of this theorem that this margin is too small to contain." The theorem states that there is no combination of positive integers x, y, z, and n, with n>2, such that xn + yn = zn, and mathematicians struggled for over 300 years to find a proof until Andrew Wiles completed one in 1995. (It is generally believed that [blank] did not actually have a valid proof.) [blank] and Blaise Pascal corresponded about probability theory.
Volume of a parallelepiped
abc
Surface area of a prism
Gottfried Leibniz
(1646-1716, German) is known for his independent invention of calculus and the ensuing priority dispute with Isaac Newton. Most modern calculus notation, including the integral sign and the use of d to indicate a differential, originated with [blank]. He also did work with the binary number system and did fundamental work in establishing boolean algebra and symbolic logic.
coefficient.
The number at the beginning of each term
Similar figure
The areas are related by the square of any corresponding length, and the volumes are related by the cube of any corresponding length. For instance, if a square has a diagonal that is 30% longer than another square, it has an area that is 1.30 × 1.30 = 1.69 times as great (69% greater). Similar reasoning applies to perimeters, side lengths, diameters, and so forth.
Kurt Gödel
(1906-1978, Austrian) was a logician best known for his two incompleteness theorems, which state that if a formal logical system is powerful enough to express ordinary arithmetic, it must contain statements that are true yet unprovable. [blank] developed paranoia late in life and eventually refused to eat because he feared his food had been poisoned; he died of starvation.
Inverse Matrices
Surface area of a pyramid
trinomial
a polynomial with three terms
degree 0.
A polynomial that is just a constant
Volume of cone
codomain
the set of possible output values is called the .
"range"
is sometimes used instead of "codomain," but "range" is also sometimes used to mean "image" (see below), so "range" is confusing and NAQT generally avoids it.
Leonhard Euler
(1707-1783, Swiss) is known for his prolific output and the fact that he continued to produce seminal results even after going blind. He invented graph theory by solving the Seven Bridges of Königsberg problem, which asked whether there was a way to travel a particular arrangement of bridges so that you would cross each bridge exactly once. (He proved that it was impsosible to do so.) [blank] introduced the modern notation for e, an irrational number about equal to 2.718, which is now called [blank]'s number in his honor (but don't confuse it for [blank]'s constant, which is different); he also introduced modern notation for i, a square root of -1, and for trigonometric functions. He proved [blank]'s formula, which relates complex numbers and trigonometric functions: ei x = cos x + i sin x, of which a special case is the fact that ei π = -1, which Richard Feynman called "the most beautiful equation in mathematics" because it links four of math's most important constants.
Surface area of a cone
Surface area of a sphere
4 x pi x r^2
Calculus operations
Derivative, integral, slope at a point, local extrema, points of inflection, and critical points
function
is an association between input values and output values, in which each input value is associated with exactly one output value. That association is often given by a formula, and it is that sort of function that this article will focus on. However, a function could be defined in other ways, such as by a table (as one might make for scientific observations) or simply by a description (for instance, your distance from home is a function of the time of day, since at each time of day you are at exactly one place, and therefore a particular distance from home).
Carl Friedrich Gauss
(1777-1855, German) is considered the "Prince of Mathematicians" for his extraordinary contributions to every major branch of mathematics. His Disquisitiones Arithmeticae systematized number theory and stated the fundamental theorem of arithmetic (every integer greater than 1 has a prime factorization that is unique notwithstanding the order of the factors). In his doctoral dissertation, he proved the fundamental theorem of algebra (every non-constant polynomial has at least one root in the complex numbers), though that proof is not considered rigorous enough for modern standards. He later proved the law of quadratic reciprocity, and the prime number theorem (that the number of primes less than n is is approximately n divided by the natural logarithm of n). [blank] may be most famous for the (possibly apocryphal) story of intuiting the formula for the summation of an arithmetic sequence when his primary-school teacher gave him the task — designed to waste his time — of adding the first 100 positive integers.
Combinations
When we want to find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; We say '3 choose 2' and write 3_C_2. 3_C_2 = 3_P_2/2!
Adding/Subtracting Matrices
Multiplying/Dividing Matrices
Area of circle
Section 2
(25 cards)