scholarly journals The Theodorus Variation

2021 ◽  
Vol 1 (2) ◽  
Author(s):  
Ewan Brinkman ◽  
Robert Corless ◽  
Veselin Jungic
Keyword(s):  
Square Roots ◽  
Open Curve ◽  
Inner Circle ◽  
Video Abstract

The Spiral of Theodorus, also known as the "root snail" from its connection with square roots, can be constructed by hand from triangles made with from paper with scissors, ruler, and protractor.  See the Video Abstract.  Once the triangles are made, two different but similar spirals can be made.  This paper proves some things about the second spiral; in particular that the open curve generated by the inner vertices monotonically approaches a circle, and that the vertices are ultimately equidistributed around that inner circle.   

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.

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

scholarly journals On the minimum gap between sums of square roots of small integers

2011 ◽  
Vol 412 (39) ◽  
pp. 5458-5465
Author(s):  
Qi Cheng ◽  
Yu-Hsin Li
Keyword(s):  
Square Roots

A Broadly Applicable 3-D Neuron Tracing Method Based on Open-Curve Snake

2011 ◽  
Vol 9 (2-3) ◽  
pp. 193-217 ◽  
Author(s):  
Yu Wang ◽  
Arunachalam Narayanaswamy ◽  
Chia-Ling Tsai ◽  
Badrinath Roysam
Keyword(s):  
Neuron Tracing ◽  
Open Curve ◽  
Tracing Method

The electrical resistivity of lithium-6

1961 ◽  
Vol 263 (1314) ◽  
pp. 407-419 ◽  
Keyword(s):  
Electrical Resistivity ◽  
Isotopic Composition ◽  
Specific Heat ◽  
Room Temperature ◽  
Natural Isotopic Composition ◽  
Square Roots ◽  
Conduction Electrons ◽  
Ionic Mass ◽  
Theoretical Predictions ◽  
Electrical Resistivities

The electrical resistivities of lithium -6 and lithium of natural isotopic composition have been studied between 4°K and room temperature. In addition, their absolute resistivities have been carefully compared at room temperature. These measurements show that the effect of ionic mass on electrical resistivity agrees with simple theoretical predictions, namely, that the properties of the conduction electrons in lithium do not depend on the mass of the ions, and that the characteristic lattice frequencies for the two pure isotopes are in the inverse ratio of the square roots of their ionic masses. A comparison with the specific heat results of Martin (1959, 1960), where the simple theory is found not to hold, indicates the possibility that anharmonic effects are present which affect the specific heat but not the electrical resistivity.

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