Centipede mathematics is a term used, sometimes derogatorily, to describe the generalisation and study of mathematical objects satisfying progressively fewer and fewer restrictions. This type of study is likened to studying how a centipede behaves when its legs are removed one by one. The term is attributed to Polish mathematician Antoni Zygmund. Zygmund is said to have described the metaphor of the centipede thus: "You take a centipede and pull off ninety-nine of its legs and see what it can do."Thus, Zygmund has been known by many mathematicians as the "Centipede Surgeon". The study of semigroups is cited as an example of doing centipede mathematics. One starts with the notion of an abelian group. First delete the commutativity restriction to obtain the concept of a group. The restriction of existence of inverses is then removed. This produces a monoid. If one now removes the restriction regarding the existence of identity, the resulting object turns out to be a semigroup. Still more legs can be removed. If the associativity restriction is also discarded one gets a magma or a groupoid. The restrictions that define an abelian group may be removed in different orders also. The study of ternary ring has been cited as an example of centipede mathematics. The progressive removal of axioms of Euclidean geometry and studying the resulting geometrical objects also illustrate the methodology of centipede mathematics. The following quote summarises the value and usefulness of the concept: "The term ‘centipede mathematics’ is new to me, but its practice is surely of great antiquity. The binomial theorem (tear off the leg that says that the exponent has to be a natural number) is a good example. A related notion is the importance of good notation and the importance of overloading, aka abuse of language, to establish useful analogies." — Gavin Wraith. (Wikipedia).
Trigonometry full course for Beginners
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of #triangles. Throughout history, #trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities, whic
From playlist Trigonometry
Trigonometry - Easy to understand 3D animation
IMPORTANT CORRECTION: The proper way to write the law of cosines is C^2 = A^2 +B^2 - 2AB cos(Ψ)
From playlist Physics
Geometry: Introduction to the Polygon (quadrilateral, pentagon, hexagon and more)
Learn the definition of polygon - a very important shape in geometry. When a polygon has a small number of sides, there is a word you use instead of "polygon". We teach you the names of polygons with 3 to 10 sides. To learn more Geometry, you can watch our playlist from the beginning:
From playlist Euclidean Geometry
Trigonometry for Beginners || Trigonometry Basics
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. This math video tutorial provides a basic introduction into #trigonometry. It covers trigonometric functions, ratios such as sine, cosine, and tangent, converting polar coordin
From playlist Trigonometry
Trigonometric Functions and the Unit Circle (Precalculus - Trigonometry 6)
The creation of the Unit Circle and how it relates to Right Triangle Trigonometry and the creation of Trigonometric Functions. Support: https://www.patreon.com/ProfessorLeonard
From playlist Precalculus - College Algebra/Trigonometry
What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry
This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t
From playlist Summer of Math Exposition 2 videos
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From playlist Knowledge
PreCalculus Full Course For Beginners
In mathematics education, #precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework. In
From playlist PreCalculus
Trigonometric Functions: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent
Oh man, what is all this sine and cosine business? What do these things even mean?! And Greek letters now? I don't know Greek! OK friend, just relax. Understanding the trig functions is as easy as pi radians. We just make some triangles and set up a few definitions. I promise it's no sweat
From playlist Trigonometry
Centipedes: The Ultimate Nopes
Start listening to 'How to Clone a Mammoth' with a 30-day Audible trial. Just go to https://www.audible.com/animalogic or text ANIMALOGIC to 500-500. Nothing quite makes you say ‘nope, nope, nope’ like a centipede. Support Animalogic on Patreon: https://www.patreon.com/animalogic Subsc
From playlist Animalogic
The House Centipede is Fast, Furious, and Just So Extra | Deep Look
Please follow us on Patreon! https://www.patreon.com/deeplook Take the PBSDS survey: https://to.pbs.org/2018YTSurvey CORRECTION, 9/26/2018: This episode of Deep Look contains an error in the scientific name of the house centipede. It is Scutigera coleoptrata, not coleoptera. We regret th
From playlist Deep Look | Series | KQED
Trigonometry 5 The Cosine Relationship
A geometrical explanation of the law of cosines.
From playlist Trigonometry
Giant Centipede | National Geographic
This centipede sheds and eats its own "skin," but is still hungry for more! ➡ Subscribe: http://bit.ly/NatGeoSubscribe #NationalGeographic #Centipedes #Bugs About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through
From playlist Trending Videos | National Geographic
Eating Myself: Giant Centipede | National Geographic
This centipede sheds and eats its own "skin" — but it's still hungry for more! ➡ Subscribe: http://bit.ly/NatGeoSubscribe #NationalGeographic #Centipedes #Bugs About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Throu
From playlist A Spooky Halloween | National Geographic
South American Centipede | National Geographic
This centipede sheds and eats its own "skin," but is still hungry for more! ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through their world-class scientists, photograp
From playlist Amazing Animals | National Geographic
CREEPY CRAWLING CENTIPEDES INFLICT EXTREME PAIN | Kings of Pain (Season 2)
Giant centipedes inject the team with a lethal sting, in this clip from Season 2, "Hundred Tiny Screams." #KingsofPain Subscribe for more from Kings of Pain and other great The HISTORY Channel shows: http://histv.co/SubscribeHistoryYT Find out more about the series and watch full epis
From playlist Kings of Pain | Official Series Playlist | History
Centipede vs. Snake | National Geographic
Are this black-headed snake's eyes bigger than its stomach? Unfortunately for the centipede, the answer is no. See All National Geographic Videos http://video.nationalgeographic.com/video/?source=4001" ➡ Subscribe: http://bit.ly/NatGeoSubscribe #NationalGeographic #Centipedes #Snakes A
From playlist Amazing Animals | National Geographic
Cannibal Cooking Lessons - Rimworld Ice Sheet Tribal Ep. 22 [Rimworld Beta 18 Ice Sheet Challenge]
In this episode of our Rimworld Ice Sheet Tribal Challenge our tribal colonist starts cooking some cannibal meals for the first time and defends his base against a group of attacking Mechanoids out on the Ice Sheet on Randy Random Extreme difficulty. ► Full Playlist: https://goo.gl/q3Cx7t
From playlist Pete Completes: Rimworld Ice Sheet Tribal Challenge - Starting with nothing [Rimworld Randy Random Extreme/Merciless]
Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704
From playlist GEOMETRY 5 - PROOFS IN GEOMETRY
Centipede vs. Grasshopper Mouse | National Geographic
The venomous mandibles of a centipede are no match for the lightning-fast reflexes of the grasshopper mouse. ➡ Subscribe: http://bit.ly/NatGeoSubscribe #NationalGeographic #Centipedes #Mice About National Geographic: National Geographic is the world's premium destination for science, exp
From playlist Vs. | National Geographic