Parabola of Descartes
In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula:
xy+ax^3+bx^2+cx=d\,
Trident curves are cubic plane curves with an ordinary double point in the real projective plane at x = 0, y = 1, z = 0; if we substitute x = x/z and y = 1/z into the equation of the trident curve, we get
ax^3+bx^2z+cxz^2+xz = dz^3,\,
which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus zero.

This is an excerpt from the article Parabola of Descartes from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
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Descartes Parabola and the Traditional Parabola - BIBSYS Brage
Master Thesis in Mathematics Education. Faculty of Mathematics and Sciences. Agder University College Spring. Descartes Parabola and the Traditional ...
brage.bibsys.no/hia/bitstream/URN:NBN:no-bibsys_brage_2522/1/master_matdid_2007_vigneswaran.pdf
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Descartes' parabola and the traditional parabola: A reconstruction of ...
B.Sc(Hons): Studied Mathematics at Jaffna University, Sri Lanka. M.Sc: Studied Applied Statistics at Peradeniya University, Sri Lanka. M.Sc: Studied ...
www.amazon.com/Descartes-parabola-traditional-reconstruction-mathematica/dp/3639146530
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ABSTRACT This study concentrates on Descartes' geometry ...
ABSTRACT. This study concentrates on Descartes' geometry, especially the Descartes' parabola and traditional parabola. Who is Descartes? Rene Descartes ...
www.uia.no/en.&/content/download/41833/553870/file/vigneswaran_07.pdf
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trident of Newton
May 1, 2004 ... Descartes studied the trident 1) of Descartes,. which has also been given the name Parabola of Descartes (although it is not a parabola).
www.2dcurves.com/cubic/cubict.html
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Judith Grabiner, Descartes and Problem-Solving, Mathematics ...
What does Descartes have to teach us about solving problems? ..... This is not a conic (it is now often called the cubical Parabola of Descartes), so the.
poncelet.math.nthu.edu.tw/disk5/js/linkage/m5.pdf
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Descartes and Problem-Solving
What does Descartes have to teach us about solving problems? ..... This is not a conic (it is now often called the cubical Parabola of Descartes), so the.
www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/1996/0025570x.di021189.02p0130a.pdf
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9783639146530: Descartes' parabola and the traditional parabola ...
AbeBooks.com: Descartes' parabola and the traditional parabola ( 9783639146530) by Theivendram, Vigneswaran and a great selection of similar New, Used ...
www.abebooks.com/9783639146530/Descartes-parabola-traditional-Theivendram-Vigneswaran-3639146530/plp
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El applet Descartes - Recursos
Descartes is an applet (a program written in Java) which can be configured. ... the following parabola graph has been created using the Descartes applet.
recursostic.educacion.es/descartes/web/ingles/presentacion/El%20applet%20Descartes.htm
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Parabola - Wikipedia, the free…
A parabola (plural parabolas or parabolae, adjective parabolic, from Greek: παραβολή) is a two-dimensional, mirror-symmetrical curve, which is approximately U ...
en.wikipedia.org/wiki/Parabola
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Functions of a Curve : Leibniz's Original Notion of Functions ...
Functions of a Curve : Leibniz's Original Notion of Functions and its Meaning for the Parabola David Dennis & Jere Confrey Mailing Address: Dr. David Dennis
www.quadrivium.info/mathhistory/Parabola.pdf
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Parabola of Descartes in science
[PDF]Descartes Parabola and the Traditional Parabola - BIBSYS Brage
Government for financing my studies and to the Agder University College for providing ... explain how Descartes' found the traditional parabola and Descartes'  ...
Investigating Parabolas and Tangents - University of Georgia
Descartes deep understanding of polynomials in two variables and the ... By changing the coefficients A, D, E, F a variety of parabolas can be produced.
Descartes' parabola and the traditional parabola: A reconstruction of ...
B.Sc(Hons): Studied Mathematics at Jaffna University, Sri Lanka. M.Sc: Studied Applied Statistics at Peradeniya University, Sri Lanka. M.Sc: Studied ...
Bucket argument - Wikipedia, the free encyclopedia
The dominant view Newton opposed was devised by René Descartes, and was supported (in part) by Gottfried Leibniz. .... In words, the surface of the water is parabolic in its dependence upon the radius. .... University of Chicago Press. p. 170.
[PDF]Omar Khayyam, Ren e Descartes and Solutions to Algebraic ...
and thus foreshadowed the analytical geometry of Descartes. We give ... theologian and the rector of the University of Utrecht, was accused of being an atheist. Omar did not seem .... tion of the circle given by (3) and the parabola given by (2).
Master thesis - University of Agder
Theivendram Vigneswaran: "Descartes' Parabola" and the Traditional Parabola. A Reconstruction of a Historical Method with the Help of the "Mathematica" ...
[PDF]Functions of a Curve : Leibniz's Original Notion of ... - Quadrivium.info
David Dennis. Parabola http://www.quadrivium.info. 2. Functions of a Curve: Leibniz's ... Descartes used equations to create a taxonomy of curves [17]. This tradition of ..... Science Education at San José State University, San José, CA. 7.
[PDF]Linkages as drawing instruments and more - eCommons@Cornell
Daina Taimina, Cornell University. (Supported by National ... When Rene Descartes (1596-1650) published his Geometry (1637) he did not create a curve by plotting points from an .... Drawing Hyperbolas and Parabolas with Links and Sliders.
[PDF]Descartes and Problem-Solving
This is not a conic (it is now often called the cubical Parabola of Descartes), ..... L., A History of Geometrical Methods, Oxford University Press, Oxford, 1940. 11.
Math Forum: Rene Descartes (Chameleon Graphing: Plane History)
Rene Descartes and his contribution to graphing in the coordinate plane. ... For example, Descartes found general equations for certain kinds of parabolas ... The Math Forum is a research and educational enterprise of the Drexel University ...
Books on the term Parabola of Descartes
Descartes: An Intellectual Biography
Descartes: An Intellectual Biography
Stephen Gaukroger, 1995
Stephen Gaukroger. 1 62.0. The work that is picked out is the 'solution of all solid problems', that is, the construction of all problems resolvable in terms of cubic or quartic equations by means of a circle and a parabola. The evidence for the ...
Descartes' parabola and the traditional parabola: A reconstruction of a historical method with the help of the...
Descartes' parabola and the traditional parabola: A reconstruction of a historical method with the help of the...
2009
B.Sc(Hons): Studied Mathematics at Jaffna University, Sri Lanka. M.Sc: Studied Applied Statistics at Peradeniya University, Sri Lanka. M.Sc: Studied Mathematics Education at Agder University, Norway.
Jan de Witt’s Elementa Curvarum Linearum: Liber Secundus
Jan de Witt’s Elementa Curvarum Linearum: Liber Secundus
Johan de Witt, A. W. Grootendorst, 2010
Descartes later solves this using a “higher” curve, namely the “trident” or “Parabola of Descartes.” We will come back to this curve in Section 5.3 of the appendix. At this point Descartes interrupts his treatment of Pappus's problem to insert an ...
Mathematics for the Nonmathematician (Dover Books on Mathematics)
Mathematics for the Nonmathematician (Dover Books on Mathematics)
Morris Kline, 1985
Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Pr...
The Investigation of Difficult Things: Essays on Newton and ...
The Investigation of Difficult Things: Essays on Newton and ...
Peter M. Harman, Alan E. Shapiro, 2002
Descartes, Pappus' problem and the Cartesian Parabola : a conjecture HENK J. M. BOS Acknowledgement Kirsti Andersen read and discussed several drafts of the present article; I am thankful for her advice and support. Sometime in 1631  ...
Descartes's Mathematical Thought
Descartes's Mathematical Thought
C. Sasaki, 2003
C. Sasaki. ED2 = GB.EA. Draw a parabola whose vertex is A and the latus rectum is GB. Let the straight line AD be connected and be cut into two equal parts at I. And let TI be extended to R (R is not always on the parabola) so that TR is equal  ...
The European Mathematical Awakening: A Journey Through the ...
The European Mathematical Awakening: A Journey Through the ...
Frank J. Swetz, 2013
Since there were very few curves in Descartes's day, each received its own fancy name. This curve was only the second ... Let us now consider Descartes's argument for the Cartesian Parabola being a geometrical curve. He gave the following ...
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Blog posts on the term
Parabola of Descartes
exzuberant: Newton and Descartes channel Dan Meyer
There's a definite pause the first time you show parametric equations to students well conditioned to Cartesian representations. I like to imagine Descartes himself staring at the equations pondering : "Why would you do that????" We're not in Kansas any more! Descartes: "Why would you do that? It's the same end result!" Here are three teaching ideas I used this year with my senior mathematics class which may supplement the traditional approach of showing the different representations are functionally equivalent.
exzuberant.blogspot.com/2012/10/newton-and-descartes-channel-dan-meyer.html
David Rabouin, “On Mathematical Style” | Barefoot Philosophers
Just as people tend to follow particular trends in the way they dress, Professor Rabouin puts forth the idea that mathematicians too adopt “theories”, “concepts” and “objects” that are in trend or in circulation. However, unlike fashion trends, these “theories” and “concepts” seem to show signs of stability: they cannot be wiped out like a fashion…
barefootphilosophers.wordpress.com/2013/01/07/david-rabouin-on-mathematical-style/
Archimedes and the area of a parabolic segment :: squareCircleZ
www.intmath.com/blog/archimedes-and-the-area-of-a-parabolic-segment/1652
The Method Man | MetaFilter
www.metafilter.com/135315/The-Method-Man
Rene Descartes: Mathematician & Philosopher | Blog, She Wrote
Rene Descartes was born on March 31, 1596. He's considered the father of modern philosophy and he was an accomplished mathematician. I chose to feature Descartes because I thought it would be a perfect tie in to some fun math lessons. You may best know his influence if you've ever graphed a line or a…
blogshewrote.org/2013/03/01/rene-descartes-mathematician-philosopher/
Rene Descartes and his Steam-Powered Robo-Dog! | John C. Wright's Journal
Part of an ongoing conversation. A reader named Gian asks: I meant to ask whether the motion of animals is completely describable by quantitative
www.scifiwright.com/2011/07/rene-descartes-and-his-steam-powered-robo-dog/
Lunar Pioneer: "Boulder 668" at Descartes C
Fig. 1.
lunarnetworks.blogspot.com/2012/07/boulder-668-at-descartes-c.html
Matthew 13:52—The (Second) Littlest Parable | NEAR EMMAUS
The other day as I was skimming through Jesus's parables in Matthew, I noticed this odd little text: 51 Συνήκατε ταῦτα πάντα; λέγουσιν αὐτῷ· Ναί. 52 ὁ δὲ εἶπεν αὐτοῖς· Διὰ τοῦτο πᾶς γραμματεὺς μαθητευθεὶς τῇ βασιλείᾳ⸃ τῶν οὐρανῶν ὅμοιός ἐστιν ἀνθρώπῳ οἰκοδεσπότῃ ὅστις ἐκβάλλει ἐκ τοῦ θησαυροῦ αὐτοῦ καινὰ καὶ παλαιά. 53 καὶ ἐγένετο…
nearemmaus.com/2013/03/06/matthew-1352-the-second-littlest-parable/
Friedrich Nietzsche: Thinker of the Issue | edifyingdiscourse
Originally written for The Fold E-zine, Issue 4, 2006 . The depicition of Nietzsche's conception of reality is a bit excitable and simplistic, however I still think that Nietzsche's Death of God is best understood through reading Anselm and Descartes. Friedrich Nietzsche will always be associated with madness. This is in no small part due…
edifyingdiscourse.wordpress.com/2011/04/23/friedrich-nietzsche-thinker-of-the-issue/
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