IB Maths Resources from British International School Phuket. Imagining the 4th Dimension Imagining extra dimensions is a fantastic ToK topic – it is something which seems counter-intuitively false, something which we have no empirical evidence to support, and yet it is something which seems to fit the latest mathematical models on string theory (which requires 11 dimensions).
Mathematical models have consistently been shown to be accurate in describing reality, but when they predict a reality that is outside our realm of experience then what should we believe? Our senses? Our intuition? Or the mathematical models? Carl Sagan produced a great introduction to the idea of extra dimensions based on the Flatland novel. Mobius strips are a good gateway into the weird world of topology – as they are 2D shapes with only 1 side. Next we can move onto the Hypercube (or Tesseract). The page allows you to model 1, then 2, then 3 dimensional traces – each time representing a higher dimensional cube. For a more involved discussion (it gets quite involved!)
Dr George Zouros - 10 Mins On TOK: Mathematics. Testing out the Monty Hall problem. Can Math Make a Better Marathon? Less than two miles from the finish of last month’s Chicago Marathon, with the race finally narrowed to a neck-and-neck duel between two Kenyan runners, the NBC television commentators began placing their bets.
It wasn’t a hard call. Abel Kirui, who hadn’t won a marathon since 2011, was visibly struggling, repeatedly falling behind and then clawing his way back. At one point, grimacing, he snatched a cup of water from a volunteer and dumped it over his head. Meanwhile, Dickson Chumba, the defending champion, was floating along with an unwrinkled brow and unvarying pace.
With half a mile to go, the camera offered a side-on shot of Kirui. Such moments are what make marathons fascinating to watch and their results impossible to predict. Purity. Lucia de B. is innocent. This internet site has been created by a group of individuals who form the “Committee for Lucia”.
None of its members are related to Lucia, nor are they from her circle of friends. They are merely individuals driven by the certainty that Lucia is the victim of a gross miscarriage of justice. # News: BBC 23-7-2010 – Can chance make you a killer? Imagine you are a hospital doctor. Richard Gill 18-4-2010 – Bureau of Lost Causes This organisation has been set up inspired by the self-less efforts by so many people over the last six years, which only just now led to the extraordinary and total rehabilitation of Lucia de Berk. Manifesto. Interactive Mathematics Miscellany and Puzzles. Front Page, Interactive Mathematics Miscellany and Puzzles. Since May 6, 1997You are visitor number 27862784 in base 11 The heart of mathematics consists of concrete examples and concrete problems.
P.R.Halmos, How to Write MathematicsAMS, 1973 Also, some pages are organized into series while others, especially the older ones, are accessible individually. Throughout the discussions at this site I refer to various titles I love and find useful enough to have them in my own library. These are collected in a table with links to the pages where they were referred to. First off, you may want to look at the page that explains to the curious the origin and nature of my logo. There is also a page where I offer a beautiful geometric problem. One page currently presents 118 different proofs of the Pythagorean Theorem which was a great fun putting together. Another page looks into different ways a specific statement may be related to a more general one. Other pages have educational content. Earth - The most beautiful equation is… Pi. Calvin.hobbes.mathreligion.gif (GIF Image, 600 × 186 pixels)
What Is Math? Math talks to blow your mind. You're Not Bad At Math, You're Just Lazy. What is Math About?: Masao Morita at TEDxKyoto 2012. Math: Human Discovery or Human Invention? So just what, in essence, is this thing called math?
In developing these numbers and systems of numbers, did we discover the hidden coding of the universe? Is mathematics, in the words of Galileo, the language of God? Or is math just a human-created system that happens to correspond with natural laws and structures? There is no definitive answer to this question, but mathematicians tend to side with one of several compelling theories. First, there is the Platonic theory. The opposing argument, therefore, is that math is a man-made tool -- an abstraction free of time and space that merely corresponds with the universe.
Several theories expand on this idea. The logistic theory, for instance, holds that math is an extension of human reasoning and logic.The intuitionist theory defines math as a system of purely mental constructs that are internally consistent.The formalist theory argues that mathematics boils down to the manipulation of man-made symbols. Is math discovered or invented? - Jeff Dekofsky.
Painted with numbers: mathematical patterns in nature. Is Math a Feature of the Universe or a Feature of Human Creation? TEDxOxford - Marcus du Sautoy - The Two Cultures: A False Dichotomy. The Psychological Difference Between $12.00 and $11.67. BBC The Story Of Maths 1 of 4 The Language Of The Universe.
TOK Maths Mrs M. Gödel, Escher, Bach - Lecture 1: Part 1 of 7. The Monty Hall Problem.