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Wau: The Most Amazing Number in the World?

This is a fantastic video from Vi Hart of Khan Academy. Watch it first and marvel at the properties of this amazing number:

Once you have watched it, watch it again – this time thinking about what number Wau might be – and why you have never heard of Wau before.

This is a great video to show to students – especially IB students, who once they have figured it out can go through the video and see why the infinite sequences, the imaginary numbers, the repeated powers etc all work. There’s one mistake in the video – which is flagged by an annotation. Turn of the annotation and see if anyone in the class spots it.

As a final exercise how about thinking about what other fantastic properties Wau has?

This links really well with the ToK question about where do we get our knowledge from – does the authority of mathematics or science allow people to be mislead more easily? A good example (in a similar vein to Wau is the “health scare” about Dihydrogen Monoxide (DHMO).

dhmo

From the website DHMO:

Dihydrogen Monoxide (DHMO) is a colorless and odorless chemical compound. The atomic components of DHMO are found in a number of caustic, explosive and poisonous compounds such as Sulfuric Acid, Nitroglycerine and Ethyl Alcohol.

Each year, Dihydrogen Monoxide is a known causative component in many thousands of deaths and is a major contributor to millions upon millions of dollars in damage to property and the environment. Some of the known perils of Dihydrogen Monoxide are:
1) Death due to accidental inhalation of DHMO, even in small quantities.
2) Prolonged exposure to solid DHMO causes severe tissue damage.
3) Excessive ingestion produces a number of unpleasant though not typically life-threatening side-effects.
4) DHMO is a major component of acid rain.
5) Gaseous DHMO can cause severe burns.

Sounds pretty scary – and something that should be regulated. And indeed the website has been the cause of numerous petitions to MPs around the world demanding that it be banned. It is however an internet hoax. All the information is correct – it’s just that it refers to……water. People often have a deference to the authority of scientific or mathematical arguments – which can make them a very powerful tool in persuading people what to believe.

For anyone who wants to know what Wau is, the answer is below in white text (highlight to reveal!)

Wau is 1. Now watch the video again!

If you enjoyed this post you might also like:

Graham’s Number – literally big enough to collapse your head into a black hole – a post about an unimaginably big number.

e’s are good – He’s Leonard Euler. – A discussion about the amazing number e.

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IB Maths Exploration Guide

IB Maths Exploration Guide

A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. Includes:

  1. Investigation essentials,
  2. Marking criteria guidance,
  3. 70 hand picked interesting topics
  4. Useful websites for use in the exploration,
  5. A student checklist for top marks
  6. Avoiding common student mistakes
  7. A selection of detailed exploration ideas
  8. Advice on using Geogebra, Desmos and Tracker.

Available to download here.

IB Exploration Modelling and Statistics Guide


IB Exploration Modelling and Statistics Guide

A 60 page pdf guide full of advice to help with modelling and statistics explorations – focusing in on non-calculator methods in order to show good understanding. Includes:

  1. Pearson’s Product: Height and arm span
  2. How to calculate standard deviation by hand
  3. Binomial investigation: ESP powers
  4. Paired t tests and 2 sample t tests: Reaction times
  5. Chi Squared: Efficiency of vaccines
  6. Spearman’s rank: Taste preference of cola
  7. Linear regression and log linearization.
  8. Quadratic regression and cubic regression.
  9. Exponential and trigonometric regression.

Available to download here.

IB HL Paper 3 Practice Questions (100 page pdf)

IB HL Paper 3 Practice Questions 

Fourteen  full investigation questions – each one designed to last around 1 hour, and totaling around 35 pages and 500 marks worth of content.  There is also a fully typed up mark scheme.  Together this is around 100 pages of content.

Available to download here.

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