So, what is the difference between the geometries of the 3 types of shapes? August 5, in Real life mathsToK maths Tags: You saved my life. Thank you very much for your help in my IA. You can read more on these questions here. There is still however something of a sleight of hand being employed here however — given an infinite length of time we have shown that Achilles would reach the tortoise, but what about reaching the tortoise in a finite length of time?

So in the first instance, Achilles runs to where the tortoise was 10 metres away. Great Maths Teaching Ideas A mixture of blog posts, videos and maths teaching resources. If at least one of the lines is flat then the surface has no curvature.

Keep up the great work! A large collection of GeoGebra Applets Some great apps on everything from the unit circle, differentiation from first principles, volume of revolutions etc.

Mandelbrot and Julia set generator. Do the words imaginary and complex make the concepts more difficult than if they had different names?

A shape with positive curvature has no such lines — and so has no parallel lines. So plain, simple but so effective. Therefore we can use the infinite summation formula for a geometric series which was derived about years after Zeno!

So using the same formula as before: Mathematics and the world. There are two slightly different versions to this paradox.

My favourite revision site is Revision Village — which has a huge amount of great resources — questions graded by level, full video solutions, practice tests, and even exam predictions.

Your site gave my extended essay a plan on how to go about it and made the journey simpler. Do proofs provide us with completely certain knowledge?

I just wanted to thank you for being a lifesaver. What is mathematical reasoning and what role does proof play in this form of reasoning?

Slow down and stop, or crunch back in on itself? An excellent resource to show the huge range of jobs that mathematicians can enter. Maths is fun A large number of maths puzzles — algebra, number and logic.

Achilles and the Tortoise The second version also makes use of geometric series. Keep up the good work, and thank you once again.

Torus The torus is a really interesting mathematical shape — basically a donut shape, which has the property of of having variable Gaussian curvature. At the heart of understanding the universe is the question of the shape of Tok mathematics universe.

A great extension for lessons on complex numbers. Your blog has been a fabulous resource! What are the different meanings of induction in mathematics and science?

The pseudosphere is a shape which is in some respects the opposite of a sphere hence the name pseudo-sphere. Oxford Education Math Studies support material.

Mathematics Illuminated Units Entire online units which explore everything from infinity, topology, game theory and extra dimensions. A sphere is an example of a shape with constant positive curvature — that means the curvature at every point is the same. The way to calculate it is to take a point on a surface, draw a pair of lines at right angles to each other, and note the direction of their curvature.

This shape has a constant negative curvature. August 27, in puzzlesReal life mathsToK maths Tags: NCTM Illuminations A large number of searchable enrichment activities, plus a large number of apps under activities to help with graphing.

Woods, your initiative is highly appreciated and needless to say, the resources on this website are helping thousands of students tremendously. The Chess Board Problem The chess board problem is nothing to do with Zeno it was first recorded about years ago but is nevertheless another interesting example of the power of geometric series.

Just today I was talking with another friend of mine who, I just found out, also happens to be following your blog.TOK: Mathematics and knowledge claims. Euler was able to make important advances in mathematical analysis before calculus had been put on a solid theoretical foundation by Cauchy and others.

Euler was able to make important advances in mathematical analysis before calculus had been put on a solid theoretical foundation by Cauchy and others. Blog and Podcast for all enthusiastic Theory of Knowledge (TOK) students and teachers (and anybody else!) as a source of inspiration.

TOK is an epistemology and critical thinking course offered by the I recently read an article about the mathematics of beauty.

Researchers found out that beauty is not in the eye of the beholder. You are currently browsing the category archive for the ‘ToK maths’ category. Projective Geometry. March 10, in ToK maths One of the most interesting questions to investigate with regards to maths Theory of Knowledge (ToK) is the relationship between maths and reality.

Mathematics describes the reality we see, the reality that. TOK: Mathematics and the real world. Is the binomial distribution ever a useful model for an actual real-world situation?

Is the binomial distribution ever a useful model for an actual real-world situation? Theory of Knowledge by Mathematical Topic Topic 1 - Algebra TOK: Mathematics and the killarney10mile.com mathematical constants (pi, e, Fibonacci numbers) appear consistently in.

Knowledge questions in mathematics include whether it is discovered or invented, and the extent to which it provides us with certain knowledge.

Helping TOK students around the world to read between the lines.

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