some punk kid's definitions
1. v. To crush or flatten to the point where the object crushed has its fluids splattered about.
2. n. The sound of something getting squished. The sound is usually wet.
3. n. In the old Nickelodeon cartoon "Aaah, Real Monsters!", a squish was when a monster mildly liked another monster. Their form of a crush.
2. n. The sound of something getting squished. The sound is usually wet.
3. n. In the old Nickelodeon cartoon "Aaah, Real Monsters!", a squish was when a monster mildly liked another monster. Their form of a crush.
1. I saw a bug crawling on the table and squished it.
2. When I stepped on a grape in the supermarket, it went "squish".
3. In one episode of "Aaah, Real Monsters", Ickis thought that Oblina had a squish on him.
2. When I stepped on a grape in the supermarket, it went "squish".
3. In one episode of "Aaah, Real Monsters", Ickis thought that Oblina had a squish on him.
by some punk kid May 1, 2005
Get the squish mug.A groundbreaking theory in biology developed by an elephant who saved a bunch of tiny people called "who". It states that all psychobiological life systems are diminutive in comparison to a greater, larger life system (life systems become infinitely big). In "Dexter's Laboratory", Dexter worked with this theory in order to analyze a civilization much smaller than ours.
by some punk kid May 1, 2005
Get the Horton's Theory of Who mug.by some punk kid May 1, 2005
Get the karma mug.A non-Euclidean geometry is any geometry that contrasts the fundamental ideas of Euclidean geometry, especially with the nature of parallel lines. Any geometry that does not assume the parallel postulate or any of its alternatives is an absolute geometry (Euclid's own geometry, which does not use the parallel postulate until Proposition 28, can be called a neutral geometry). The first non-Euclidean geometries arose in the exploration of disputing Euclid's notorious Fifth Postulate, which states that if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which are the angles less than two right angles. Critics of the "parallel postulate" do not argue that it is a mathematical fact. Instead, they do not find it as brief, simple, and self-evident as postulates are supposed to be. Furthermore, the converse of the parallel postulate, corresponding to Proposition 27, Book I, of Euclid's Elements, has a proof, which fueled the argument that the parallel postulate should be a theorem.
Many logically equivalent statements include, but are not limited to:
1. Through a given point not on a given line, only one parallel can be drawn to the given line. (Playfair's Axiom)
2. A line that intersects one of two parallel lines intersects the other also.
3. There exists lines that are everywhere equidistant from one another.
4. The sum of the angles of a triangle is equal to two right angles.
5. For any triangle, there exists a similar noncongruent triangle.
6. Any two parallel lines have a common perpendicular.
7. There exists a circle passing through any three noncollinear points.
8. Two lines parallel to the same line are parallel to each other.
For two thousand years, geometers attempted to prove the parallel postulate, but every proof failed due to an assumption made similar to the ones above or just faulty thinking. Probably the most interesting of these are the proofs of the 17th-18th century Italian geometer Girolamo Saccheri. He tried to prove it using a reductio ad absurdum argument. By proving that the sum of the angles of a triangle cannot be greater than or less than 180 degrees, he would have achieved his goal. He successfully proved that they cannot be greater that 180 degrees, but could not find a contradiction of the latter case. He ended his proof and denied himself the opportunity to be history's first non-Euclidean geometer. This honor would be saved for two later mathematicians, Janos Bolyai and Nicolai Lobachevsky.
Both contemporaries of Carl Gauss, Lobachevsky and Bolyai did pioneering work in hyperbolic geometry, which keeps Euclid's other four postulates in tact, but supposes that through any given point not on a given line, infinitely many lines can be drawn parallel to that given line. As opposed to Euclidean geometry, which asserts that the distance between any two lines is constant, hyperbolic geometry visually means that lines curve toward each other. They discovered this to be logically coherent and a feasible alternative to Euclidean geometry. It is safe to assume that these facts were known to previous mathematicians such as Gauss and Adrien-Marie Legendre, both contributing much to elliptic functions and having conducted experiments that led them to conclude that the sum of the angles of a triangle can be less than 180 degrees. Sadly, Legendre did this in an attempt to prove the parallel postulate (hence disposing of his chance as first non-Euclidean geometer), and Gauss never published his findings in order to avoid controversy (Immanuel Kant, a prominent German philosopher of the late 1700's, in his "Critique of Pure Reason", stated the Euclidean geometry is the true geometry of the universe and to contradict it is to contradict thought itself.) Gauss did, however, discover much of differential geometry and potential theory.
Bernhard Riemann, a student of Gauss, in a famous lecture in 1854, established Riemannian geometry and discussed modern concepts such as curvature, manifolds, and (Riemannian) metrics. By giving a formula for a family of Riemannian metrics on the unit ball in Euclidean space, Riemann constructed infinitely many possible non-Euclidean geometries and provided the logical foundation for elliptic geometry, which states that through a given point not on a given line, no parallel lines exist. Visually, we can interpret this as lines curving toward each other. We cannot call Riemann, however, the sole inventor of elliptic geometry since his theory extends to all geometries, including the default Euclidean n-space. The ideas for elliptic and, mainly, hyperbolic geometry continued to develop by mathematicians of the later half of the century, such as Eugenio Beltrami, Felix Klein, and Henri Poincare. Such geometries have proven useful to the development of topology in the 20th century and to physics, notably in Albert Einstein's theory of general relativity.
Though interesting, much of non-Euclidean geometry is far too advanced to be taught in high school (or even at the undergraduate level in college!) along with basic Euclidean geometry. In order to grasp it fully and do original work in it, one must have a good working knowledge of multivariable calculus, linear and abstract algebra, real and complex analysis, and topology.
Many logically equivalent statements include, but are not limited to:
1. Through a given point not on a given line, only one parallel can be drawn to the given line. (Playfair's Axiom)
2. A line that intersects one of two parallel lines intersects the other also.
3. There exists lines that are everywhere equidistant from one another.
4. The sum of the angles of a triangle is equal to two right angles.
5. For any triangle, there exists a similar noncongruent triangle.
6. Any two parallel lines have a common perpendicular.
7. There exists a circle passing through any three noncollinear points.
8. Two lines parallel to the same line are parallel to each other.
For two thousand years, geometers attempted to prove the parallel postulate, but every proof failed due to an assumption made similar to the ones above or just faulty thinking. Probably the most interesting of these are the proofs of the 17th-18th century Italian geometer Girolamo Saccheri. He tried to prove it using a reductio ad absurdum argument. By proving that the sum of the angles of a triangle cannot be greater than or less than 180 degrees, he would have achieved his goal. He successfully proved that they cannot be greater that 180 degrees, but could not find a contradiction of the latter case. He ended his proof and denied himself the opportunity to be history's first non-Euclidean geometer. This honor would be saved for two later mathematicians, Janos Bolyai and Nicolai Lobachevsky.
Both contemporaries of Carl Gauss, Lobachevsky and Bolyai did pioneering work in hyperbolic geometry, which keeps Euclid's other four postulates in tact, but supposes that through any given point not on a given line, infinitely many lines can be drawn parallel to that given line. As opposed to Euclidean geometry, which asserts that the distance between any two lines is constant, hyperbolic geometry visually means that lines curve toward each other. They discovered this to be logically coherent and a feasible alternative to Euclidean geometry. It is safe to assume that these facts were known to previous mathematicians such as Gauss and Adrien-Marie Legendre, both contributing much to elliptic functions and having conducted experiments that led them to conclude that the sum of the angles of a triangle can be less than 180 degrees. Sadly, Legendre did this in an attempt to prove the parallel postulate (hence disposing of his chance as first non-Euclidean geometer), and Gauss never published his findings in order to avoid controversy (Immanuel Kant, a prominent German philosopher of the late 1700's, in his "Critique of Pure Reason", stated the Euclidean geometry is the true geometry of the universe and to contradict it is to contradict thought itself.) Gauss did, however, discover much of differential geometry and potential theory.
Bernhard Riemann, a student of Gauss, in a famous lecture in 1854, established Riemannian geometry and discussed modern concepts such as curvature, manifolds, and (Riemannian) metrics. By giving a formula for a family of Riemannian metrics on the unit ball in Euclidean space, Riemann constructed infinitely many possible non-Euclidean geometries and provided the logical foundation for elliptic geometry, which states that through a given point not on a given line, no parallel lines exist. Visually, we can interpret this as lines curving toward each other. We cannot call Riemann, however, the sole inventor of elliptic geometry since his theory extends to all geometries, including the default Euclidean n-space. The ideas for elliptic and, mainly, hyperbolic geometry continued to develop by mathematicians of the later half of the century, such as Eugenio Beltrami, Felix Klein, and Henri Poincare. Such geometries have proven useful to the development of topology in the 20th century and to physics, notably in Albert Einstein's theory of general relativity.
Though interesting, much of non-Euclidean geometry is far too advanced to be taught in high school (or even at the undergraduate level in college!) along with basic Euclidean geometry. In order to grasp it fully and do original work in it, one must have a good working knowledge of multivariable calculus, linear and abstract algebra, real and complex analysis, and topology.
Other examples of a non-Euclidean geometry include affine geometry, the modern projective geometries of Girard Desargues, Blaise Pascal, Michel Chasles, Jean-Victor Poncelet, and Jakob Steiner, the line geometry of Julius Plucker, the algebraic geometry of Frederigo Enriques and Francesco Severi, the enumerative geometry of Hermann Schubert, and the taxicab geometry of Hermann Minkowski.
by some punk kid October 18, 2006
Get the Non-Euclidean Geometry mug.Just hanging around. Modeled after the term used to describe the curve/shape assumed by a suspended cord or cable.
by some punk kid March 20, 2005
Get the catenary mug.Braggadocious emcee from Harlem with incredible lyrics and an even more incredible vocabulary. Born Mohandes Dewese, Kool Moe Dee used to kick mad routines with The Treacherous 3 in the early 80's. He is credited with inventing the speed rap (The Treacherous 3 & Spoonie Gee "The New Rap Language") and popularizing freestyling (New Year's Battle with Busy Bee in December '81). After going solo with his single "Turn It Up" and releasing his debut album "I'm Kool Moe Dee", Moe Dee regularly worked with mega-producer Teddy Riley and made great fashion statements with his leather suits and giant blind man shades.
Kool Moe Dee is most famous for his phenomenal battles with Busy Bee, Run-D.M.C. (alongside Special K on the seminal rap television show "Graffiti Rock"), and, most of all, LL Cool J. Ignorant suckas like to say that LL won the battle with "Jack The Ripper". However, Moe Dee lyrically eviscerated LL with "Let's Go" and "Death Blow". Needless to say, Kool Moe Dee was never much of a commercial mainstay. Nevertheless, Kool Moe Dee has had major hits with "Wild Wild West", "How Ya Like Me Now", "They Want Money", and "I Go To Work". Recently, he dropped the "e" in "Moe" and wrote a book called "There's A God On The Mic: The True 50 Greatest MC's", where he put himself at number 5 behind Big Daddy Kane, KRS-One, Rakim, and Melle Mel. Although never humble, Kool Moe Dee knows what he's talking about. He is one of rap's first deep lyricists, he has battle skills like no one else, and if you want an example of real, unadulterated hip-hop, especially from back in the day, then... KOOL MOE DEE IS THE BEST TO LISTEN TO!
Kool Moe Dee is most famous for his phenomenal battles with Busy Bee, Run-D.M.C. (alongside Special K on the seminal rap television show "Graffiti Rock"), and, most of all, LL Cool J. Ignorant suckas like to say that LL won the battle with "Jack The Ripper". However, Moe Dee lyrically eviscerated LL with "Let's Go" and "Death Blow". Needless to say, Kool Moe Dee was never much of a commercial mainstay. Nevertheless, Kool Moe Dee has had major hits with "Wild Wild West", "How Ya Like Me Now", "They Want Money", and "I Go To Work". Recently, he dropped the "e" in "Moe" and wrote a book called "There's A God On The Mic: The True 50 Greatest MC's", where he put himself at number 5 behind Big Daddy Kane, KRS-One, Rakim, and Melle Mel. Although never humble, Kool Moe Dee knows what he's talking about. He is one of rap's first deep lyricists, he has battle skills like no one else, and if you want an example of real, unadulterated hip-hop, especially from back in the day, then... KOOL MOE DEE IS THE BEST TO LISTEN TO!
"Whoever said rap is not work is ludacris.
Whoever said it must be new to this.
When you hear me,
You'll compare me
To a prophet for profit, not merely
Writing extra rhymes for recreation.
Each rhyme's a dissertation.
You wanna know my occupation?
I get paid to rock the nation."
-"I Go To Work"
Oh, and Moe Dee did not bite Spyder D's "How Ya Like Me Now."
Whoever said it must be new to this.
When you hear me,
You'll compare me
To a prophet for profit, not merely
Writing extra rhymes for recreation.
Each rhyme's a dissertation.
You wanna know my occupation?
I get paid to rock the nation."
-"I Go To Work"
Oh, and Moe Dee did not bite Spyder D's "How Ya Like Me Now."
by some punk kid February 10, 2005
Get the kool moe dee mug." The Father of Algebra." (780 - 845 C.E.) Abu Abdullah Muhammad bin Musa Al-Khwarizmi was a Persian mathematician and astronomer. He wrote the famous book "Al-Kitab Al-Mukhtasar fi Hisab Al-Jabr Wa'l-Muqabala" ("The Compendious Book on Calculation by Completion and Balancing") in 830. The book offered a systematic and logical approach to solving linear and quadratic equations. This became the premise of algebra. He is also responsible for introducing the Hindu-Arabic numerals to the West, thus becoming the golden standard in global mathematics. He also refined Ptolemy's theories on geography to design the first map of the then "known world", wrote on spacial, time-mechanical devices such as the clock, astrolabe, and sundial, made a table of trigonometric functions, and geometrically interpreted the conic sections.
Sure. Newton created the calculus. Liebniz refined it. Kepler popularized it. Lambert generalized it. And Euler organized it. If it wasn't for Al-Khwarizmi, however, most people wouldn't even understand basic arithmetic.
by some punk kid April 21, 2005
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