Tag Archive for: geometry
A Trick to Memorizing Trig Special Angle Values Table
/
3 Comments
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…
An Introduction to Theorema Primum
Introduction
Whilst no doubt most frequenters of "Physics Forums" will be familiar with Nicolaus Copernicus as the scientist who advanced the (at the…
Physical Applications of the “Tan Rule”
Introduction
Every secondary school student who has encountered trigonometry in his/her Math syllabus will most likely have come across the sine, cosine,…
Investigating Some Euler Sums
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…
Computing the Riemann Zeta Function Using Fourier Series
Euler's amazing identity
The mathematician Leonard Euler developed some surprising mathematical formulas involving the number ##\pi##. The most famous…
Geometry of Side-side-angle (SSA) and Impossible Triangles
What is the ambiguous case?
In high school geometry, the idea of proofs is often first introduced to American students. A common task is to use a basic…
Learn the Geometry of Mathematical Quantum Field Theory
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…
When Simple Geometry Unveils Deep Math
Introduction
It is a remarkable fact that consideration of very elementary concepts in geometry often leads quickly into deep and unexpected mathematical…
How to Self Study Geometry for Students
Geometry is one of the oldest parts of mathematics. It has been studied and advanced by the greatest minds humankind has to offer. It has been described…
Higher Prequantum Geometry V: The Local Observables – Lie Theoretically
This article discusses how the previous considerations naturally follow the concepts of local observables of local field theories and of…
Higher Prequantum Geometry IV: The Covariant Phase Space – Transgressively
The Euler-Lagrange ##p##-gerbes discussed in the previous article are singled out as being exactly the right coherent refinement…
Higher Prequantum Geometry III: The Global Action Functional – Cohomologically
The previous article ended with the concept of classical locally variational field theories, of which a class of examples are…
Higher Prequantum Geometry II: The Principle of Extremal Action – Comonadically
The previous article motivated the importance of considering "pre-quantum field theory" in-between classical and quantum field…
Higher Prequantum Geometry I: The Need for Prequantum Geometry
Before proceeding with a discussion of the super p-brane sigma models, whose emergence from the superpoint I discussed in the previous article,…