Articles written by Isaac M. McPhee
Showing 1-100 of 310 Articles
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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!
|
|
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
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
The Rhind Papyrus
The Rhind Papyrus is perhaps the best known demonstration of the mathematics of ancient Egypt during the Second Intermediate Period.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
Hyperbolic Geometry
One of the most common families of non-Euclidean geometry is hyperbolic geometry - a self-consistent geometry of "obtuse" curvature.
|
|
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
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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."
|
|
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.
|
|
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.
|
|
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.
|
|
Discrete Mathematics
Discrete mathematics, most commonly finding applications in computer sciences, are used to define groups of numbers which are finite, or "countable."
|
|
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.
|
|
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.
|
|
Combinatorics
Combinatorics refers to fundamental operations which may be carried out amongst various mathematical sets, offering a tremendous number of potential uses.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
The Rise of John F. Kennedy
John F. Kennedy, born to a life of privilege, suffered from great medical problems through much of his life, but certainly found success nonetheless.
|
|
The Eisenhower Presidency
Newly elected President Dwight David Eisenhower found himself facing a continuing war in Korea and the beginnings of what would become the Cold War.
|
|
Eisenhower's Military Career
Dwight David Eisenhower, prior to becoming President of the United States, served the U.S. Army for more than 40 years, achieving the highest rank of any officer.
|
|
Harry Truman's Second Term
Harry Truman, despite his current status as one of America's greatest Presidents, found his second term dogged by the lowest Presidential poll numbers ever recorded.
|
|
Harry Truman's First Term
Harry S Truman, remembered today as a generally great President, made a number of very memorable decisions during his first term, including that to use "the bomb."
|
|
The Rise of Harry S Truman
Harry Truman's rise to political power, first in Missouri and then nationally, was certainly unlikely. Despite the uphill battle, this man fought his way to success.
|
|
The Franklin Roosevelt Presidency
Franklin Delano Roosevelt is surely one of the most important political figures of the twentieth century, whether one agrees with his policies or not.
|
|
The Rise of Franklin Roosevelt
Franklin Delano Roosevelt, America's 32nd President, was born to a life of luxury and success in New York, which was aided by his personal charisma and intelligence.
|
|
The Presidency of Herbert Hoover
Beginning in the very first year of his Presidency, the Great Depression became the most memorable feature of Herbert Hoover's Presidency.
|
|
Hoover's Road to the White House
Herbert Hoover's first foray into politics came when President Harding named him Commerce Secretary in 1920. It was from here that the road to the White House was paved.
|
|
The Rise of Calvin Coolidge
Soft-spoken Calvin Coolidge was an unlikely choice for Vice President of the United States, but in 1920, he made it to this position nonetheless.
|
|
The Presidency of Calvin Coolidge
After the sudden death of Warren G. Harding, Calvin Coolidge became the unlikely 30th President of the United States, attempting to bring a nation back together.
|
|
The Rise of Herbert Hoover
Herbert Hoover, perhaps best known as having presided over the Great Depression, lived a very interesting, exciting and undeniably impressive life before the Presidency.
|
|
The Warren G. Harding Presidency
Warren G. Harding is generally remembered in a negative light, as one of the least effective Presidents in American History... but was he really so awful?
|
|
The Rise of Warren G. Harding
Warren G. Harding, a traditional conservative, engineered a prodigious rise from obscure local newspaper man to national politician in a very short period of time.
|
|
Euler's Mathematical Contributions
Leonard Euler was surely the most prolific and important mathematician of the eighteenth century, and perhaps of all time, with accomplishments far too numerous to count.
|
|
The Life of Leonard Euler
Leonard Euler left his indelible mark on almost every area of mathematics, publishing hundreds upon hundreds of mathematical papers and volumes throughout his career.
|
|
Review of Smoot's Ear
In the 2007 book "Smoot's Ear: The Measure of Humanity," Robert Tavernor takes an interesting and novel approach to understanding how mankind measures things.
|
|
President Wilson's Second Term
Woodrow Wilson had no choice but to send America to war in 1917, though he did so in hopes that he could perhaps prevent all such wars in the world's future.
|
|
President Wilson's First Term
The first half of Woodrow Wilson's 8 years in office focused on Domestic policies such as the tariff, the money issue, and antitrust legislation, along with keeping Ameri
|
|
The Rise of Woodrow Wilson
Despite a late start in terms of education, Woodrow Wilson nevertheless spent much of his life before the Presidency as one of America's great scholars.
|
|
William Taft on the Supreme Court
When President Harding appointed William Howard Taft to the Supreme Court in 1920, he helped him to fulfill a lifelong dream.
|
|
The Presidency of William Taft
Theodore Roosevelt's plan to place William Taft into the Presidency as a hand-picked successor did not turn out as well as he had hoped, as Taft had a mind of his own.
|
|
The Rise of William Howard Taft
From the earliest times of his career in law, William Howard Taft dreamed of being on the Supreme Court, and his life in public service served served to get him there.
|
|
A Survey of the Fourth Dimension
Treading a fine line between math, art and science, this capable, entertaining, and colorful book challenges the reader to begin to comprehend a fourth dimension.
|
|
The Five Platonic Solids
Demonstrating the often-overlapping sciences of mathematics, philosophy, physics, and theology, the platonic solids have historically been seen as fundamentally important
|
|
Roosevelt's Post Presidency
Despite having his hand-picked successor in office, Theodore Roosevelt's life after the Presidency was dominated in part by his opposition to his own political party.
|
|
The Presidency of Teddy Roosevelt
Earning himself a place on Mt. Rushmore was not easy, but Theodore Roosevelt worked hard at the Presidency, focusing on getting things done and on initiating reform.
|
|
The Early Years of Teddy Roosevelt
Theodore Roosevelt, prior to becoming America's 26th President, lived an exciting life of politics, civil service, academics, and frontiersman.
|
|
The Presidency of William McKinley
Before his assassination in 1901, William McKinley found a good deal of success in the office of the President, being the first incumbent since Ulysses S. Grant to win re
|
|
The Rise of William McKinley
William McKinley, the Ohioan who would later become President, began his life in politics early, and lived much of his life in service to his country.
|
|
President Benjamin Harrison
Benjamin Harrison's four years in the office of President has been largely forgotten in the century since. His legacy is mixed, despite a strong legislative agenda.
|
|
The Rise of Benjamin Harrison
Benjamin Harrison, grandson of President William Henry Harrison, climbed quickly up the political ladder, from local politics to national recognition.
|
|
Grover Cleveland's Second Term
Finally defeating Benjamin Harrison on his second attempt, Grover Cleveland returned to the White House, but times had changed.
|
|
President Cleveland's First Term
Grover Cleveland's first term as President of the United States saw him attempting to reform the Federal Government, though he did little legistlating.
|
|
The Rise of Grover Cleveland
Grover Cleveland's path to the White House did not truly begin until elected Mayor of Buffalo, New York in 1881. Three years later, he would be President.
|
|
Chester A. Arthur in Office
Chester A. Arthur, 21st President of the United States, proved himself to be far more independent and above reproach than his opponents could have anticipated.
|
|
The Politics of Chester A. Arthur
Chester A. Arthur, soon to be 21st President of the United States, was a loyal member of the stalwart faction of Republican Politics throughout his rise to the Vice-Presi
|
|
The Slow Death of James Garfield
Though his assassine was convicted of his murder, the true blame for the death of James Garfield has been shown to rest, in part, on his doctors themselves.
|
|
The Politics of James A. Garfield
James A. Garfield worked very hard throughout his life, succeeding at many things, including his education, his military career, and, of course, politics.
|
|
The Art of Charles Willson Peale
Charles Willson Peale painted some of the most memorable portraits in American history during the period surrounding the revolution, and spawned a family of artists.
|
|
The Rutherford B. Hayes Presidency
Rutherford B. Hayes is not among the most well-known Presidents of the United States, but he played an important role in determining the shape of the union after the war.
|
|
The Controversial Election of 1876
Though Rutherford B. Hayes trailed in both popular and electoral votes, a congressional compromise named him President on one of the most controversial elections in Ameri
|
|
The Rise of Rutherford B. Hayes
Rutherford B. Hayes achieved the Presidency in part because his early life offered very little in the way of scandal. He was a capable lawyer and a wartime hero.
|
|
The Circle of Willis
The Circle of Willis is a vital formation of arteries at the base of the brain which supplies all thought processes with the necessary fuel.
|
|
The Human Stomach
The stomach is a marvelous piece of biological engineering - exactly what is needed by the body to break down food with powerful acids while protecting the body.
|
|
The Physiology of Skin
Human skin is a highly complex, highly important organ, serving many different functions within the body and being absolutely essential for human life as we know it.
|
|
The Many Purposes of Saliva
Saliva serves many purposes within the mouth, such as a digestive aid and acid neutralization, both of which are vital to the human physiology.
|
|
The Parathyroid Glands
The parathyroid gland is an essential part of the human anatomy, regulating the crucial calcium supply to the entire body.
|
|
The Politics of Ulysses S. Grant
There has been much debate over the legacy of President Grant over the years, with some naming him among the worst, while others finding things to admire.
|
