Video on Simplices and Simplicial Complexes

Professor Wildberger is extremely kind to upload his videos which would be very useful to any Math student studying Topology. Simplices / Simplicial Complexes are usually the first chapter in a Algebraic Topology book.

Check out also Professor Wildberger’s book on Rational Trigonometry, something that is quite novel and a new approach to the subject of Trigonometry. For instance, it can be used for rational parametrisation of a circle.

Pick’s Theorem Proof (Video)

This is an excellent video I found on Youtube by Professor Wildberger on the proof of Pick’s Theorem. It is easy enough for a high school student to understand!

Pick’s Theorem is a formula A=I+\frac{B}{2}-1 which gives the area of a simple polygon whose vertices lie on points with integer coordinates. Surprisingly, it is a relatively modern theorem, the result was first described by Georg Alexander Pick in 1899.

Using Pick’s Formula, the area of the above polygon is A=I+\frac{B}{2}-1=7+\frac{8}{2}-1=10. We can also see that it is the sum of two triangles A=\frac{1}{2}(4)(2)+\frac{1}{2}(4)(3)=10.

Amazing Formula!

Source: http://en.wikipedia.org/wiki/Pick’s_theorem


Featured book:

Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers (MSRI Mathematical Circles Library)

A recent visitor to my website bought this book. Highly interesting and suitable for parents of young children. Three to seven is a critical period where the brain develops, hence learning about how to teach math to preschoolers is of great significance for young parents.

This book is a captivating account of a professional mathematician’s experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even “work” at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn’t ask and then answer a question, but shows us a problem–be it mathematical or pedagogical–and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. This book does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

AlgTop1: One-dimensional objects

This is a continuation of the series of Algebraic Topology videos. Previous post was AlgTop 0.

Professor Wildberger is an interesting speaker. He holds some unorthodox views, for instance he doesn’t believe in “real numbers” or “infinite sets”. Nevertheless, his videos are excellent and educational. Highly recommended to watch!

The basic topological objects, the line and the circle are viewed in a new light. This is the full first lecture of this beginner’s course in Algebraic Topology, given by N J Wildberger at UNSW. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways.


Featured book:

Divine Proportions: Rational Trigonometry to Universal Geometry

Author: NJ Wildberger

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.