Articles related to "Euclidean Geometry"
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.
spherical geometry • surface of a globe • euclidean geometry • non euclidean geometry • geodesic
While most people are familiar with foundational geometrical principles which are essentially "flat," non-Euclidean geometry plays an important role in many cases.
spherical geometry • surface of a globe • euclidean geometry • non euclidean geometry • geodesic
Euclidean v Non-Euclidean Geometry
While most people are far more familiar with the basic principles of Euclidean geometry, scientists have come to discover that the shape of our universe is non-Euclidean.
euclid of alexandria • greek mathematicians • euclidean geometry • non-euclidean geometry • the shape of the universe
While most people are far more familiar with the basic principles of Euclidean geometry, scientists have come to discover that the shape of our universe is non-Euclidean.
euclid of alexandria • greek mathematicians • euclidean geometry • non-euclidean geometry • the shape of the universe
Hyperbolic Geometry
One of the most common families of non-Euclidean geometry is hyperbolic geometry - a self-consistent geometry of "obtuse" curvature.
hyperbolic geometry • saddle-shape geometry • hyperparallelism • euclidean geometry • non euclidean geometry
One of the most common families of non-Euclidean geometry is hyperbolic geometry - a self-consistent geometry of "obtuse" curvature.
hyperbolic geometry • saddle-shape geometry • hyperparallelism • euclidean geometry • non euclidean geometry
A Definition of Fractal Geometry
One of the interesting developments of modern mathematics is the exploration of new forms of geometry which do not adhere to "standard" definitions.
fractal geometry • chaos theory • coastline analogy for fractals • self-similarity • non-euclidean geometry
One of the interesting developments of modern mathematics is the exploration of new forms of geometry which do not adhere to "standard" definitions.
fractal geometry • chaos theory • coastline analogy for fractals • self-similarity • non-euclidean geometry
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.
trigonometry • sine • cosine • tangent • secant
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.
trigonometry • sine • cosine • tangent • secant
Carl Friedrich Gauss
Brief biography of Carl Friedrich Gauss, one of the greatest and most influential mathematicians in history. He made advances in number theory.
carl friedrich gauss • gauss biography • gauss german mathematician • gauss physicist • gauss number theory of series
Brief biography of Carl Friedrich Gauss, one of the greatest and most influential mathematicians in history. He made advances in number theory.
carl friedrich gauss • gauss biography • gauss german mathematician • gauss physicist • gauss number theory of series
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.
commutativity • commutative • noncommutativity • noncommutative • mathematical physics
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.
commutativity • commutative • noncommutativity • noncommutative • mathematical physics
Euclid's Fifth Axiom
Very few seemingly incontrovertible mathematical statements throughout history have wreaked quite as much havoc as Euclid's controversial fifth axiom.
euclid's fifth axiom • the parallel postulate • non-euclidean geometry • proving euclid's fifth axiom • karl friedrich gauss
Very few seemingly incontrovertible mathematical statements throughout history have wreaked quite as much havoc as Euclid's controversial fifth axiom.
euclid's fifth axiom • the parallel postulate • non-euclidean geometry • proving euclid's fifth axiom • karl friedrich gauss
Euclid's First Axiom
Euclid's first axiom, concerning points and straight lines, contains hidden depth that one might miss upon a cursory glance, and which is important to his geometry.
euclid's axioms • euclid's first axiom • ancient greek mathematicians • history of geometry • euclidean geometry
Euclid's first axiom, concerning points and straight lines, contains hidden depth that one might miss upon a cursory glance, and which is important to his geometry.
euclid's axioms • euclid's first axiom • ancient greek mathematicians • history of geometry • euclidean geometry
Euclid's Third Axiom
Euclid's third axiom describes how a simple circle, one of the most important figures in geometry, can be constructed using only a point and a line.
euclid's third axiom • definition of a circle • euclidean geometry • history of geometry • history of mathematics
Euclid's third axiom describes how a simple circle, one of the most important figures in geometry, can be constructed using only a point and a line.
euclid's third axiom • definition of a circle • euclidean geometry • history of geometry • history of mathematics
Gravity and General Relativity
In essence, Einstein's General Theory of Relativity was an entirely new theory of gravity, replacing the centuries-old theories of Isaac Newton.
curved spacetime • gravity • general relativity • what is gravity • the equivalence principle
In essence, Einstein's General Theory of Relativity was an entirely new theory of gravity, replacing the centuries-old theories of Isaac Newton.
curved spacetime • gravity • general relativity • what is gravity • the equivalence principle
The 3-4-5 Rule is the Pythagorean Theorem
The Pythagorean theorem is the basis for the 3-4-5 rule. This simple math equation is a carpenter's tool used to find or verify the squareness of a room or object.
the 3-4-5 rule • pythagorean theorem • control lines • tile or laminate floors • concrete forms
The Pythagorean theorem is the basis for the 3-4-5 rule. This simple math equation is a carpenter's tool used to find or verify the squareness of a room or object.
the 3-4-5 rule • pythagorean theorem • control lines • tile or laminate floors • concrete forms
Examples of Mathematical Fractals
Clever mathematicians over the years have devised some interesting and visually stunning examples of fractal figures which help them to better understand this concept.
fractal geometry • what is a fractal • self-similarity • benoit mandelbrot • mandelbrot set
Clever mathematicians over the years have devised some interesting and visually stunning examples of fractal figures which help them to better understand this concept.
fractal geometry • what is a fractal • self-similarity • benoit mandelbrot • mandelbrot set
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
lie group • lie algebra • differential calculus • differentiability • continuity
The term "lie group" (pronounced "lee") refers to certain classifications of manifolds - a highly technical, difficult form of mathematics, but one with great pragmatic
lie group • lie algebra • differential calculus • differentiability • continuity
Euclid's Life and the Elements
Brief account of Euclid's work in relation to geometry and the key postulates from his famous book the Elements.
euclid's life and the elements • euclid • euclid elements • greek mathematician • father of geometry
Brief account of Euclid's work in relation to geometry and the key postulates from his famous book the Elements.
euclid's life and the elements • euclid • euclid elements • greek mathematician • father of geometry
Introduction to Topology
Topology is the study of the mathematics of various shapes; it defines their features and the possible manipulations they can undergo while retaining their shape.
topology • donut into coffee cup • homeomorphism • leonard euler • seven bridges of konigsberg
Topology is the study of the mathematics of various shapes; it defines their features and the possible manipulations they can undergo while retaining their shape.
topology • donut into coffee cup • homeomorphism • leonard euler • seven bridges of konigsberg
On the Development of Letterpress Typefaces
The earliest typefaces were made to be almost indistinguishable from hand calligraphy, while "modern" type attempts to sever the connection to handwriting entirely.
type • typography • printing • calligraphy • gutenberg
The earliest typefaces were made to be almost indistinguishable from hand calligraphy, while "modern" type attempts to sever the connection to handwriting entirely.
type • typography • printing • calligraphy • gutenberg
The Purpose of Calculus
Created nearly simultaneously by two mathematical geniuses, calculus to many is little more than a pointless numerical exercise. It's uses, though, are vast in number.
calculus • isaac newton • gotfried leibnitz • history of calculus • functions
Created nearly simultaneously by two mathematical geniuses, calculus to many is little more than a pointless numerical exercise. It's uses, though, are vast in number.
calculus • isaac newton • gotfried leibnitz • history of calculus • functions
Web Scavenger Hunts for Students
Web scavenger funts are a fun way to teach research and critical thinking skills while students learn about a particular topic, such as the Revolutionary War. This article lists many fun web sites.
web hunts • treasure hunts • scavenger hunts • computers • technology
Web scavenger funts are a fun way to teach research and critical thinking skills while students learn about a particular topic, such as the Revolutionary War. This article lists many fun web sites.
web hunts • treasure hunts • scavenger hunts • computers • technology
The Legacy of General Relativity
When Einstein published his General Theory of Relativity, surely even he could not be fully aware of the profound effect it would have on the scientific community.
general relativity • results of general relativity • albert einstein • what is general relativity • curved spacetime
When Einstein published his General Theory of Relativity, surely even he could not be fully aware of the profound effect it would have on the scientific community.
general relativity • results of general relativity • albert einstein • what is general relativity • curved spacetime
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