Articles written by Isaac M. McPhee
Showing 1-50 of 310 Articles
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The Game of Life
In 1970, British mathematician John Conway invented "The Game of Life," which became increasingly popular throughout the nineteen seventies among math enthusiasts.
Mar 5, 2009
- Isaac M. McPhee
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The Sieve of Eratosthenes
Throughout mathematical history, thinkers have attempted to come up with a great many methods by which to discover prime numbers. Eratosthenes' was perhaps the simplest.
Mar 5, 2009
- Isaac M. McPhee
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Using Roman Numerals
How long until Superbowl CII? What is LXIV + DCM? These are questions that most modern individuals could not reasonably know how to answer.
Feb 20, 2009
- Isaac M. McPhee
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Medved's Ten Big Lies
Through his daily radio show heard throughout the United States, Michael Medved has built a reputation of being one of talk radio's most intelligent and informed pundits.
Feb 20, 2009
- Isaac M. McPhee
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Who Was Archimedes?
Archimedes is highly regarded in many circles. It was his remarkable mind - unrivaled but for a few individuals in history - which led to his legendary historical status.
Jan 28, 2009
- Isaac M. McPhee
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Commutativity in Mathematics and Nature
In mathematics, commutativity is a long word describing a very simple concept. A commutative process is one which can be reversed with no change in result.
Jan 23, 2009
- Isaac M. McPhee
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Ludwig Boltzmann's Statistics
When Atomic Theory began to grow in popularity during the nineteenth century, it did so in part thanks to the mathematical work of Austrian Physicist Ludwig Boltzmann.
Jan 14, 2009
- Isaac M. McPhee
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Chaos Theory and Water Droplets
Researchers at MIT have been working to explore the always-difficult world of chaos theory by way of a rather simple experiment involving bouncing water droplets.
Dec 26, 2008
- Isaac M. McPhee
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The Mathematics of the Beatles
In October of 2008, a math professor at Dalhousie University in Nova Scotia revealed an astonishing discovery: He had used math to understand the music of the Beatles!
Dec 1, 2008
- Isaac M. McPhee
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New Findings in Beauty and Mathematics
Mathematicians - like all scientists - are often on the lookout for a certain element of "beauty" in their formulas. But what does this beauty actually look like? And sh
Nov 24, 2008
- Isaac M. McPhee
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The Math and Physics of Golf Balls
New methods of computation are allowing mathematicians and physicists to finally begin to truly understand the physics of airflow around golf balls in flight.
Nov 24, 2008
- Isaac M. McPhee
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Complex Numbers
Complex numbers are numbers which are combinations of any real number plus the imaginary number. While difficult to comprehend, imaginary numbers are quite real.
Nov 7, 2008
- Isaac M. McPhee
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Computer-Assisted Proofs
Much of mathematics, both theoretical and practical, has been built up throughout the centuries in the language of proofs - formal statements of mathematical reasoning.
Nov 7, 2008
- Isaac M. McPhee
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What are Irrational Numbers?
Irrational numbers, though of great importance in many branches of mathematics, are difficult concepts for the human mind to grasp, for they are real, yet infinite.
Nov 5, 2008
- Isaac M. McPhee
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The Bernoulli Family Tree
The Bernoulli family, through four generations in the 16th and 17th centuries, was one of the most prominent and important mathematical and scientific families.
Nov 5, 2008
- Isaac M. McPhee
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Difference Equations and Modern Physics
Whereas in much of physics scientists tend to rely on differential equations to describe phenomena, certain physical theories find success by denying continuity.
Oct 15, 2008
- Isaac M. McPhee
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Nanotechnology Mimics Nature's Adhesive
Scientists in recent weeks have begun to pave the way toward using nanotechnology for very practical purpose: Keeping things from falling off walls.
Oct 9, 2008
- Isaac M. McPhee
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The Rhind Papyrus
The Rhind Papyrus is perhaps the best known demonstration of the mathematics of ancient Egypt during the Second Intermediate Period.
Sep 27, 2008
- Isaac M. McPhee
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What is Differential Geometry?
Differential Geometry is a form of advanced mathematics which deals with the properties of continuous manifolds in multiple dimensions, using basic tools of calculus.
Sep 27, 2008
- Isaac M. McPhee
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The Poincare Conjecture
Discovered by French mathematician Henri Poincare in the first decade of the 20th century, the Poincare Conjecture is used to define spherical topology.
Sep 27, 2008
- Isaac M. McPhee
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Squaring the Circle
The problem of finding a square which has the exact same area as a given circle is a problem which for centuries eluded some of history's greatest mathematicians.
Aug 20, 2008
- Isaac M. McPhee
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Spherical Geometry
While most people are familiar with foundational geometrical principles which are essentially "flat," non-Euclidean geometry plays an important role in many cases.
Aug 20, 2008
- Isaac M. McPhee
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Hyperbolic Geometry
One of the most common families of non-Euclidean geometry is hyperbolic geometry - a self-consistent geometry of "obtuse" curvature.
Aug 20, 2008
- Isaac M. McPhee
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Lie Groups
The term "lie group" (pronounced "lee") refers to certain classifications of manifolds - a highly technical, difficult form of mathematics, but one with great pragmatic
Aug 20, 2008
- Isaac M. McPhee
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Numerical Integration
Numerical integration is a form of calculus which seeks to find the area under either a simple or a complex curve - more difficult than it sounds.
Aug 20, 2008
- Isaac M. McPhee
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Mathematical Identities
Over the course of one's mathematical education, they inevitably are forced to memorize a great many mathematical identities, maybe without even realizing it.
Aug 20, 2008
- Isaac M. McPhee
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The Prisoner's Dilemma
Developed by Merrill Flood and Melvin Dresher at RAND in 1950, the case of the "Prisoner's Dilemma" has become a classic example of a game theory conundrum.
Aug 20, 2008
- Isaac M. McPhee
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The Nash Equilibrium
Brought to the attention of the mathematical community by famed mathematician John Nash in 1951, the Nash Equilibrium is an important element of game theory.
Aug 20, 2008
- Isaac M. McPhee
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What is Game Theory?
Game theory is a branch of applied mathematics which relates to strategy and prediction of behavior; a complicated science with a diverse range of applications.
Aug 20, 2008
- Isaac M. McPhee
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The Infinite and the Infinitesimal
To many it is surely surprising just how complicated the idea of "infinity" can truly be, for, oddly enough, it can exist both in various forms and in various "sizes."
Aug 14, 2008
- Isaac M. McPhee
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The Importance of Significant Digits
In math and science, it can often be far too easy to exaggerate a number's accuracy, leading to mathematical errors. For these reasons, significant digits are important.
Aug 14, 2008
- Isaac M. McPhee
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The Basics of Venn Diagrams
Created by British Philosopher John Venn in 1881, Venn diagrams have made their way into almost every facet of set-based thought, well beyond mathematics.
Aug 14, 2008
- Isaac M. McPhee
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The Unit Circle
The so-called unit circle is one of the key tools of trigonometry. At its simplest, it is merely a circle which has a center point at (0,0) and a radius of one.
Aug 14, 2008
- Isaac M. McPhee
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Discrete Mathematics
Discrete mathematics, most commonly finding applications in computer sciences, are used to define groups of numbers which are finite, or "countable."
Aug 14, 2008
- Isaac M. McPhee
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Basic Equations for Lines
One of the fundamental tools which should be remembered from a basic algebra class is how to mathematically describe any line on a graph.
Aug 14, 2008
- Isaac M. McPhee
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What is an Algorithm?
Algorithms are rather obscure, difficult to define sets of instructions, whether logical or mathematical, which allow one to accomplish a given task.
Aug 14, 2008
- Isaac M. McPhee
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Combinatorics
Combinatorics refers to fundamental operations which may be carried out amongst various mathematical sets, offering a tremendous number of potential uses.
Aug 14, 2008
- Isaac M. McPhee
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Continuous Functions
Out of the many principles necessary for understanding the mathematics of calculus, one of the most important (and deceptively simple), is that of continuity.
Jul 31, 2008
- Isaac M. McPhee
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Modular Arithmetic
In what way are clocks, musical scales, sine waves and long division related? They all rely on a form of mathematics known as modular arithmetic.
Jul 31, 2008
- Isaac M. McPhee
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A History of the Fields Medal
When by his last will Alfred Nobel instituted the Nobel Prize in 1895 to recognize great human endeavors, he neglected to make allowance for achievements in mathematics.
Jul 16, 2008
- Isaac M. McPhee
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Basic Trigonometric Principles
The most basic trigonometric operations, finding sines, cosines, and tangents, may seem rather tedious and without purpose at first, but these are essential to calculus.
Jul 16, 2008
- Isaac M. McPhee
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The Value of the Abacus
Thousands of years prior to the invention of the mechanical and electronic calculator, mathematicians all over the world made use of abaci - a surprisingly helpful tool.
Jul 16, 2008
- Isaac M. McPhee
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Forms of Mathematical Symmetry
In Mathematics and many of applications thereof, there is great importance placed on the idea of symmetry and the methods of transforming one thing into another.
Jul 16, 2008
- Isaac M. McPhee
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What is a Limit?
One of the first things that a student of calculus must learn upon delving into this intimidating mathematical subject, is how to find the limit of an equation.
Jul 16, 2008
- Isaac M. McPhee
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The Nixon Presidency
Richard Nixon is surely best remembered for the Watergate scandal and subsequent resignation. There is certainly much more to his time in office than that, however.
Jul 7, 2008
- Isaac M. McPhee
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The Comeback of Richard Nixon
Richard Milhous Nixon, an impressive politician from California, left the Vice Presidency in 1960 in hopes of attaining the White House for himself.
Jul 7, 2008
- Isaac M. McPhee
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The Rise of Richard M. Nixon
Richard Milhous Nixon showed signs of great political potential very early on in life, and certainly would live up to that potential in later life.
Jul 7, 2008
- Isaac M. McPhee
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Lyndon Johnson's Presidency
Taking over the Presidential reins after the tragic assassination of Kennedy, Lyndon Johnson attempted to continue Kennedy's policies, while adding in many of his own.
Jun 23, 2008
- Isaac M. McPhee
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The Rise of Lyndon Johnson
Lyndon Baines Johnson, who would later become the 36th President of the United States, began his career as a teacher in Texas before moving on to politics.
Jun 23, 2008
- Isaac M. McPhee
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The Kennedy Presidency
John F. Kennedy's Presidency lasted just under three years, but in this time he was able to achieve several victories, both foreign and domestic.
Jun 18, 2008
- Isaac M. McPhee
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