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# Browsing by Subject "Mathematics"

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• (Keene State College, 4/9/2016)
Since ancient times, mathematicians have been aware that the perimeter of a circle divided by its diameter yields a constant quantity. The value was first measured to be about 3; however, the exact value, known as pi, was ...
• (Keene State College, 4/9/2016)
There are formulas that will give all triples of integers a, b, and c that satisfy the Pythagorean Theorem a^2 + b^2 = c^2. It was only recently that it was proved that the equation a^n + b^n = c^n has no integer solutions ...
• (Keene State College, 04/11/2015)
Begin with any positive integer n. Write it as the sum of two smaller positive integers, say a and b. Compute the product ab. Repeat the same step in any order for each of the smaller numbers a and b. Continue this ...
• (Keene State College, 4/9/2016)
The objective of this talk is to introduce three methods that transform a given convergent infinite series into another infinite series that converges to the same sum and that approximates the sum with fewer terms. This ...
• (Keene State College, 10/11/2017)
Have you ever wondered about the actual properties of complex numbers? Have you ever enjoyed or pondered at their computations and their geometric representation? This presentation will investigate some interesting properties ...
• (Keene State College, 10/11/2017)
In this presentation, we will investigate the application of a branch of higher mathematics called group theory to peg solitaire. To play peg solitaire, a peg 'jumps' over an adjacent peg. The jumped peg is then removed ...
• (Keene State College, 10/11/2017)
In high school, every geometry student learns the Pythagorean Theorem, which states that a triangle ABC with sides a, b, and c is a right triangle if and only if a^2 + b^2 = c^2. A Pythagorean triple is a triple of three ...
• (Keene State College, 4/9/2016)
A perfect parallelogram is defined as a parallelogram whose sides and diagonals are positive integers. We first look at three separate cases one of which is a general parallelogram where the sides and diagonals satisfy the ...
• (Keene State College, 4/9/2016)
When you add two positive integers, the sum is a positive integer. Every positive integer, except number one, is the sum of two positive integers, but which positive integer is the sum of two or more consecutive positive ...
• (Keene State College, 10/11/2017)
Abstract: A convex figure in the plane is a set of points that completely contains the line segment that joins any two points of the figure. Convex sets have the property that given any direction, parallel lines in that ...
• (Keene State College, 04/11/2015)
Elliptic Curves will be explored from a mathematical perspective as well as from a cryptographic perspective, where they have important applications to modern information security. We will address what elliptic curves ...
• (Keene State College, 4/9/2016)
Determining procedures for finding solutions to polynomial equations has long been an important pursuit in the study of mathematics. One example, introduced in most high school algebra courses, is the method for solving ...
• (Keene State College, 10/11/2017)
: We live in what we think of as a three-dimensional world. We justify this by noting that if a point is selected as the origin and three mutually perpendicular real number lines are drawn through the origin, then each ...
• (Keene State College, 04/11/2015)
Nathaniel Bowditch (1773-1838) was an American mathematician who pulled himself out of a life of poverty through self-education. Fulfilling an early passion for mathematics, he taught himself advanced topics by reading the ...
• (Keene State College, 4/9/2016)
Abstract: The algebraic equation x^2 = 1 has two solutions x = -1, 1. We assume the existence of a new number u, called the unipotent, which has the property that u does not equal -1 or 1 and that u^2 = 1. The hyperbolic ...
• (Keene State College, 10/11/2017)
I am working this semester tutoring a 5th grader at Wheelock School, who's math skills are above grade level. Part of our time together involves engaging him in mathematical investigations that stimulate him to experiment ...
• (Keene State College, 04/11/2015)
Given an area enclosed by a convex curve, the problem is to find the optimal arrangement of N points within the boundary such that the minimum distance between any two points is as large as possible. This particular problem ...
• (Keene State College, 10/11/2017)
The Chokwe people of central and southern Africa create designs in sand called sona drawings. In a typical mathematical manner, we ask whether these drawings can be created without lifting a finger from the sand. However, ...
• (Keene State College, 04/11/2015)
A repunit (a contraction of ?repeating units?) is a natural number in which every digit is a one. This talk will discuss two interesting properties that are related to repunits and prime numbers. The first property is the ...
• (Keene State College, 04/11/2015)
A quartic equation is one of the form ax4+bx3+cx2+dx+e=0. There is a formula that will give the solutions to this equation in terms of a, b, c, d, and e, but it is very cumbersome to use. This talk will present a method ...