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The Trident of Newton (or just “Trident”) is a cubic curve defined by the equation 
ax3 + bx2 + cx + d = xy,
where coefficients a, b, c, d, are real constants and a ≠ 0, ad ≠ 0.
The curve, which is sometimes called a Cartesian parabola  or Parabola of Descartes (even though it isn’t a parabola) is an esoteric algebraic curve (“algebraic” means that it can be described with polynomials).
The above graph was created with Desmos. Click on the link and you’ll be able to specify different values for the constants.
History of The Trident of Newton
According to MacTutor , both Newton and Descartes studied the curve, although it was Newton who named it “trident.” The trident appears in Newton’s Introduction to the Quadrature of Curves. The text was translated into English by by John Harris in 1710 . Newton states that the properties of the trident include:
- Four infinite legs (i.e., the four ends of the curve tend to infinity),
- Two tending towards contrary parts (i.e., the y-axis is an asymptote).
Other Meaning of Trident
As well as describing a plane curve, Newton used a trident symbol to describe Bismuth. Newton made creative and unorthodox use of alchemical symbols, most of which he created himself .
 Trident of Newton. Retrieved March 3, 2022 from: https://archive.lib.msu.edu/crcmath/math/math/t/t328.htm
 Lawrence, D. (1972). A Catalog of Special Plane Curves. Dover Publications.
 Shikin, E. (2014). Handbook and Atlas of Curves. CRC Press.
 MacTutor. Trident of Newton. Retrieved March 3, 2022 from: https://mathshistory.st-andrews.ac.uk/Curves/Trident/#:~:text=The%20trident%20is%20the%2066,two%20tending%20towards%20contrary%20parts%20.
 Harris, J. (1710). INTRODUCTION TO THE QUADRATURE OF CURVES. London.
 Symbol Guide. Retrieved March 3, 2022 from: https://webapp1.dlib.indiana.edu/newton/reference/symbols.do
Stephanie Glen. "Trident of Newton" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/trident-of-newton/
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