Continued Fractions Courses and Certifications

Fibonacci Numbers and the Golden Ratio

273 reviews

In this course, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to compute any Fibonacci number from powers of the golden ratio.

• Coursera
• 9 hours 26 minutes
• On-Demand
• Paid Course

• Best of All Time

Insights into Mathematics

Turn Angles, Continued Fractions and Approximate Geometry - WildTrig: Intro to Rational Trigonometry

Explore turn angles and continued fractions to approximate geometry, using the Euclidean algorithm for angles and circular arcs. Learn about the natural unit of angle and its applications.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Manfred Denker: Toral Automorphisms Driven by Continued Fractions

Explore toral automorphisms driven by continued fractions, discussing Poisson limits, homoclinic groups, and Steiner's theorem in dynamical systems and number theory.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

First Expansive Returns and Cross Sections

Explore the concept of first expansive power in continued fraction-like interval maps and its connection to cross sections of geodesic flow on hyperbolic surfaces, with proof of a key conjecture.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Descendants of the Mother of All Continued Fractions

Explore the mathematical procedure of contraction in continued fractions, from Seidel's 1855 method to modern applications, including new superoptimal continued fractions with fast convergence and superior approximation properties.

• YouTube
• 43 minutes
• On-Demand
• Free Video

Mathologer

How Did Ramanujan Solve the Strand Puzzle?

Explore Ramanujan's genius through an infinite fraction puzzle, delving into continued fractions, Pell equations, and the Euclidean algorithm. Gain unique insights into mathematical concepts and problem-solving techniques.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Mathologer

The Golden Ratio Spiral - Visual Infinite Descent

Explore number-associated spirals, infinite descent proofs, and continued fractions. Debunk golden ratio myths while gaining insights into number properties through visual representations.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Eddie Woo

Differential Calculus - Trigonometric Functions and Limits

Master trigonometric derivatives and limits through convergence analysis, radian measure applications, and advanced proof techniques for calculus mastery.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Renormalisation via Continued Fractions in Symbolic Dynamics

Explorez la renormalisation via les fractions continues en dynamique symbolique avec Valérie Berthe. Plongez dans les mathématiques avancées et découvrez les liens entre géométrie, dynamique et théorie des nombres.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Insights into Mathematics

Greek Number Theory - Math History - NJ Wildberger

Explore ancient Greek number theory, including primes, perfect numbers, and the Fundamental Theorem of Arithmetic. Learn about Euclidean algorithms, continued fractions, and Pell's equation.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Insights into Mathematics

Greek Number Theory - Math History - NJ Wildberger

Explore ancient Greek number theory, including squares, primes, and the Fundamental Theorem of Arithmetic. Learn about Euclidean algorithms, continued fractions, and Archimedes' Cattle Problem.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Wrath of Math

The Most Unhinged Way to Solve Quadratic Equations

Discover an unconventional method for solving quadratic equations using continued fractions, exploring Bombelli's approximation and advanced algebraic techniques beyond traditional approaches.

• YouTube
• 23 minutes
• On-Demand
• Free Video

ICTP Mathematics

Summer School in Dynamics - Introductory and Advanced

Explore fundamental and advanced concepts in dynamical systems through circle maps, ergodic theory, and renormalization techniques with expert-led lectures and hands-on tutorials.

• YouTube
• 1 day 1 hour 23 minutes
• On-Demand
• Free Video

ICTP Mathematics

The Rogers-Ramanujan Identities and the Icosahedron - Lecture 4

Exploración profunda de las identidades Rogers-Ramanujan, su conexión con el icosaedro y sus implicaciones en teoría de números, formas modulares, combinatoria y teoría de campos conformes.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

ICTP Mathematics

Rotations of the Circle and Renormalization - Lecture 2

Explore advanced concepts in dynamical systems, focusing on circle rotations and renormalization techniques with expert insights from Corinna Ulcigrai.

• YouTube
• 53 minutes
• On-Demand
• Free Video