Geometry Articles

Tag Archive for: geometry

trig special functions

A Trick to Memorizing Trig Special Angle Values Table

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In calculus classes when you are asked to evaluate a trig function at a specific angle, it's 99.9% of the time at one of the so-called special angles we…
Theorema Primum tutorial

An Introduction to Theorema Primum

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Introduction Whilst no doubt most frequenters of "Physics Forums" will be familiar with Nicolaus Copernicus as the scientist who advanced the (at the…
tan rule

Physical Applications of the “Tan Rule”

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Introduction Every secondary school student who has encountered trigonometry in his/her Math syllabus will most likely have come across the sine, cosine,…
euler sums

Investigating Some Euler Sums

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So, why only odd powers? Mostly because the even powers were solved by Leonard Euler in the 18th century. Since the “mathematical toolbox” at that…
Fourier Series Riemann Zeta Function

Computing the Riemann Zeta Function Using Fourier Series

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Euler's amazing identity The mathematician Leonard Euler developed some surprising mathematical formulas involving the number ##\pi##. The most famous…
impossible triangles

Ambiguous SSA Case in Triangles — Law of Sines Explained

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What is the ambiguous case? In U.S. high schools, students are often introduced to geometric proofs for the first time. A common task is to use a small…
qtf_geometry

Learn the Geometry of Mathematical Quantum Field Theory

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This is the first chapter in a series on Mathematical Quantum Field Theory.The next chapter is 2. Spacetime. 1. Geometry The geometry of physics…
geometrysimple

When Simple Geometry Unveils Deep Math

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Introduction It is a remarkable fact that consideration of very elementary concepts in geometry often leads quickly into deep and unexpected mathematical…
geometry1

Pure Geometry Study Guide: Books & Roadmap for Students

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Introduction to Pure Geometry Why study pure geometry? Geometry is one of the oldest parts of mathematics. It has been studied and advanced by the greatest…
prequantumgeometry5

Higher Prequantum Geometry V: The Local Observables – Lie Theoretically

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 This article discusses how the previous considerations naturally follow the concepts of local observables of local field theories and of…
prequantumgeometry4

Higher Prequantum Geometry IV: The Covariant Phase Space – Transgressively

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  The Euler-Lagrange ##p##-gerbes discussed in the previous article are singled out as being exactly the right coherent refinement…
prequantumgeometry3

Higher Prequantum Geometry III: The Global Action Functional – Cohomologically

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  The previous article ended with the concept of classical locally variational field theories, of which a class of examples are…
prequantumgeometry2

Higher Prequantum Geometry II: The Principle of Extremal Action – Comonadically

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  The previous article motivated the importance of considering "pre-quantum field theory" in-between classical and quantum field…
prequantumgeometry

Higher Prequantum Geometry I: The Need for Prequantum Geometry

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 Before proceeding with a discussion of the super p-brane sigma models, whose emergence from the superpoint I discussed in the previous article,…