Vowels and Consonants

2016 ◽  
Author(s):  
Joseph Mazur
Keyword(s):  
French Mathematician ◽  
Symbolic Algebra ◽  
Square Roots ◽  
Intimate Link ◽  
And Algebra ◽  
Infinite Sum ◽  
Greek Geometry

This chapter focuses on the evolution of the vowel–consonant notation. In particular, it discusses François Viète's contribution to algebra through his use of vowels to represent unknowns and consonants to represent known quantities. Viète, a French mathematician, expressed his famous computation for π‎ in proposition II of his Isagoge. Even Christoff Rudolff and Nicolas Chuquet had no proper notation for expressing such an infinite sum of nested square roots. Viète was showing us an intimate link between Greek geometry and algebra, a link from the mathematics of lines, figures, and solids to the underlying channels of symbolic algebra. The chapter also considers Viète's work on what are now called “homogeneous equations” as well as the significance of his lettering system to symbolic algebra.

The Timid Symbol

2016 ◽  
Author(s):  
Joseph Mazur
Keyword(s):  
Cube Root ◽  
Square Root ◽  
Square Roots ◽  
Fourth Root ◽  
And Algebra ◽  
The Right

This chapter discusses the evolution of symbols as used in mathematics. It begins by considering Michael Stifel's Arithmetica Integra, a treatise on arithmetic and algebra that included several symbols such as “plus,” “minus,” and “radix,” but not a sign for “equals.” The oldest notation for radicals (square roots, cube roots, and so on) dates back to about 1480, when a dot placed before the radicand was used to signify a square root: two dots for the fourth root, and three dots for the cube root. By 1524, the dot evolved into a blackened point with a tail bent upward to the right. Algebra at that time was concerned with solving cubic and higher degree polynomials. The chapter also examines Stifel's edition of Christoff Rudolff's Die Coss (1525) and the sign used by Nicolas Chuquet to symbolize the square root.

scholarly journals Geometry and Algebra of the Deltoid Map

2021 ◽  
Vol 128 (1) ◽  
pp. 25-39
Author(s):  
Joshua P. Bowman
Keyword(s):  
And Algebra

scholarly journals Algebraic singularities of scattering amplitudes from tropical geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Scattering Amplitudes ◽  
Natural Language ◽  
Tropical Geometry ◽  
Cluster Algebras ◽  
Finite Alphabet ◽  
Square Root ◽  
Finite Sets ◽  
Yang Mills ◽  
Square Roots ◽  
Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

Branching processes and functional differential equations determining steady-size distributions in cell populations

1995 ◽  
Vol 32 (01) ◽  
pp. 1-10
Author(s):  
Ziad Taib
Keyword(s):  
Differential Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Differential Equations ◽  
Cell Populations ◽  
Size Distributions ◽  
Multitype Branching Process ◽  
Functional Differential ◽  
Intuitive Interpretation ◽  
Infinite Sum

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

scholarly journals Finding of principle square root of a real number by using interpolation method

2018 ◽  
Vol 7 (1) ◽  
pp. 77-83
Author(s):  
Rajendra Prasad Regmi
Keyword(s):  
Real Number ◽  
Positive Real Number ◽  
Interpolation Method ◽  
Square Root ◽  
Real Numbers ◽  
Positive Real ◽  
Unknown Quantity ◽  
Square Roots

There are various methods of finding the square roots of positive real number. This paper deals with finding the principle square root of positive real numbers by using Lagrange’s and Newton’s interpolation method. The interpolation method is the process of finding the values of unknown quantity (y) between two known quantities.

Why Square Roots are Irrational

1986 ◽  
Vol 93 (3) ◽  
pp. 213-214 ◽  
Author(s):  
William C. Waterhouse
Keyword(s):  
Square Roots
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