Rheticus and 17th Century Trig Tables - WildTrig: Intro to Rational Trigonometry - N J Wildberger
Explores Rheticus' groundbreaking 17th-century trigonometric tables, highlighting their historical significance and impact on classical trigonometry's development and application.
Astronomy and Trigonometry in India - Math History
Explore ancient Indian contributions to astronomy and trigonometry, including Brahma Gupta's work and the development of sign tables, in this insightful mathematical history lecture.
Trigonometric Dual Laws and the Parallax Formula - Universal Hyperbolic Geometry
Explore trigonometric dual laws and the Right parallax formula in Universal Hyperbolic Geometry. Learn about Pythagoras' theorem, Cross dual law, and zero quadrance/spread theorems.
Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry
Explore classical theorems of Menelaus and Ceva in universal hyperbolic geometry, along with new results on triangle proportions and alternate spreads. Learn about ratios, distances, and quadrances in triangular geometry.
Thales' Theorem, Right Triangles + Napier's Rules - Universal Hyperbolic Geometry
Explores Thales' theorem and Napier's rules in universal hyperbolic geometry, focusing on right triangles. Covers key concepts like quadrea, spreads, and proofs, with practical exercises for deeper understanding.
The Cross Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger
Explores the Cross law in Universal Hyperbolic Geometry, proving it with a polynomial identity and demonstrating its application to equilateral triangles. Includes exercises and comparisons to Euclidean geometry.
The Spread Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry
Explores the Spread law in universal hyperbolic geometry, including its definition, relation to Euclidean geometry, proof, and implications. Covers key concepts like quadrance, spread duality, and quadrea.
Quadrance and Spread - Universal Hyperbolic Geometry
Introduces algebraic definitions of quadrance and spread in Universal Hyperbolic Geometry, comparing with Rational Trigonometry and exploring main laws and exercises in this advanced mathematical framework.
Number Theory and Algebra in Asia - Math History - NJ Wildberger
Explores number theory, algebra, and astronomy in ancient Chinese, Indian, and Arab mathematics, highlighting key figures and their contributions to mathematical development.
Fourier Series
Explore Fourier Series: representation of functions, L2 integral norm, and MATLAB examples. Gain practical insights into engineering mathematics with real-world applications.
Infinite Dimensional Function Spaces and Fourier Series
Explore infinite dimensional function spaces and Fourier series, covering inner product spaces, orthogonal functions, and complex functions in engineering mathematics.
Fourier Transforms
Explore the powerful Fourier transform, its applications in engineering, and its connection to orthogonal basis functions and Fourier series in this comprehensive mathematical lecture.
Solving Trigonometric Equations Using Square Roots and Identities - Practice Test Full Solutions
Comprehensive guide to solving trigonometric equations using square roots and identities, featuring step-by-step solutions, unit circle approaches, and general solution techniques for various trig functions.
Learn Precalculus - Comprehensive Problem-Solving Guide
Comprehensive precalculus review covering algebra, trigonometry, and geometry, with problem-solving examples from James Stewart's Calculus textbook. Ideal preparation for calculus studies.
Comprehensive Trigonometry and Conic Sections Tutorial
Comprehensive trigonometry tutorial covering problem-solving techniques, conic sections, and live demonstrations. Includes downloadable notes and interactive Q&A sessions.
Prelinear Algebra - Essential Concepts for Linear Algebra
Comprehensive introduction to vectors, trigonometry, and geometry as foundational concepts for Linear Algebra, with applications in various fields like physics, economics, and machine learning.
An Interesting Infinite Sum, Featuring Fourier Series
Explore the derivation of a closed form for the infinite sum cos(n)/n^4 using Fourier series, featuring integration by parts and coefficient analysis.
An Interesting Trigonometry Problem - Featuring Roots of Unity
Explore a classic trigonometric identity involving multiples of pi/11, derived using roots of unity. Gain insights into advanced mathematical concepts and problem-solving techniques.
Integral of (ln(cos x))^2
Explore advanced integration techniques using Fourier series to solve a challenging definite integral involving logarithms and trigonometric functions.
So Many Factorials
Explore advanced mathematical techniques to evaluate complex factorial series, utilizing central binomial coefficients, generating functions, and trigonometric integrals for problem-solving.
A Trigonometric Integral
Explore strategies for solving complex trigonometric integrals using recursively defined sequences, enhancing your mathematical problem-solving skills.