Classic Mathematical Joke

A mathematician finishes a large meal and says: √(-1/64)

Adam Richman from the TV show Man versus Food

Confused?

√-1 = i            and as we all know         √64 = 8

Hence, the mathematician actually said i/8 (I over ate).

To quote the late great Frank Carson "It's the way I tell 'em".

Fibonacci Numbers and all that

This week we have been looking at number patterns in class and finished off the week drawing flowers based on the Fibonacci sequence. Here is the relevant video which can also be found on Vi Hart's excellent blog.

We also had a peek at fractals via Sierpinski's Triangle and Pascal's Triangle.

This also linked neatly into the Ulam Spiral and Prime numbers.

Hopefully, all this activity helped demonstrate the overall inter-connectedness of mathematics and how it can be utilised in both explaining and describing the world we live in. An excellent source of further information can be found on the web pages of Dr. Ron Knott at the University of Surrey.

Daisies with 13, 21, 34, 55 or 89 petals are quite common.
Here we have a Shasta daisy with 21 petals.

Seasonal Mathematics

Now the Christmas tree is up and decorated I thought it time for some seasonal mathematics.

So, the question is, how many presents all together?

GOOGLE's 13th Birthday

Today is Google's 13th birthday. How many QI facts do you know about the number 13?

How about this one to get you started -

13 (along with 5 and 563) is one of only three known Wilson primes. Named after English mathematician John Wilson, this is a prime number p such that p² divides (p − 1)! + 1, where "!" denotes the factorial function (ie. 13x12x11x10 ...x1).

i.e. (13-1)! + 1 / (13x13) is an integer

12! + 1 / 169 = 479001601 / 169 = 2834329

Try to come up with a list of interesting facts without using Wikipedia!

Happy Birthday

Today, Saturday 24th September, would have been Jim Henson's 75th Birthday. In honour of the creator of the Muppets and Sesame Street I bring you Count von Count!

The Count's main purpose is educating children on simple mathematical concepts, most notably counting. The Count has a love of counting (arithmomania); he will count anything and everything, regardless of size, amount, or how much annoyance he is causing the other Muppets or human cast.

The Count's favourite number is 34969 can you work out the prime factors of this number? Cookie Monster's favourite number is rumoured to be Pi. Is it possible to work out the prime factors of Pi? If so what are they, and if not why not?

Exploding People

Still on the subject of exploding people watch the following clip and then try to solve the problems.

Assuming the man weighs 12 stone and that the average density of a human being is 1.4 g/cm cubed what is his volume?

If the man was broken into pieces approximately 2cm by 2cm by 2cm (approx. 1 inch cubes) how many pieces would the FBI agents have to pick up?

Estimate the weight of the ear that Walter Bishop holds up in the video.

SPLAT!

Here is the answer to the exploding brain problem.

43% of 9 lb = 3.87 lb

1 kg is approx. 2.2 lb so woman's brain weighs 1.76 kg

If 1 kg of water is equivalent to 1000 cubic centimetres then the volume of blood is approx. 1760 cubic centimetres. If this is spread at a thickness of 1mm (ie. 0.1 cm) then the area covered would be 17591 square centimetres or 1.76 square metres.

In reality blood is thicker than water (ie denser) so less area would be covered.

Forensic Science

Can't see the above video? Click here.

Having watched the above video the following question arises.

If the average small female head weighs 9lb, and given that the human brain only accounts for approximately 43% of this weight, when the woman's head exploded what would be the surface area covered in blood.

Hint - Make the following assumptions
The brain is completely made of blood which has the same weight as water.
The blood is dispersed at an average thickness of 1mm
Convert all measurements to metric ie. 9lb = ? kg

Answer on Friday 16th September

Prize awarded for largest mathematical proof

Prize awarded for largest mathematical proof - physics-math - 09 September 2011 - New Scientist

In early November, Michael Aschbacher, an innovator in the abstract field of group theory at the California Institute of Technology in Pasadena will receive the $75,000 Rolf Schock prize in mathematics from the Royal Swedish Academy of Sciences for his pivotal role in proving the Classification Theorem of Finite Groups, aka the Enormous Theorem.

Solomon estimates that only a few mathematicians in the world (including Aschbacher) understand the complete proof. It was a punishing read, says Mark Ronan, an honorary professor of mathematics at University College London. "Some of Aschbacher's proofs were just diabolically difficult," he adds.

Writing Big Numbers

Can you write this number in digits and/or in standard notation (as a number times 10 to the power of something)?

Pierre de Fermat's Last Theorem

"'I have discovered a truly remarkable proof but this margin is too small to contain it,' Pierre de Fermat famously wrote on margin of his copy of the Arithmetica by Diophantus of Alexandria back in 1637. The proof the French mathematician and lawyer was referring to was for his theorem in which he states that no three positive integers x, y, and z can satisfy the equation

where n is an integer greater than two.

Fermat's Last Theorem, also called Fermat's great theorem, was his best known work and to commemorate the 410th birth anniversary of the founder of the modern theory of numbers Google has put up a doodle inspired by the theorem."