distribution of primes on calculator
It all started out of a conversation between students during a short break in one of my maths classes. The focus of their conversation was a poster I have in my classroom which lists all the prime numbers...
CAS - why not?
In the mathematical world, CAS stands for computer algebra system, not creativity, action & service. Any calculator (I prefer the word "device") with CAS is not allowed to be used on an IB exam. But,...
Is Reality a Mathematical Structure?
The Swedish-American cosmologist Max Tegmark thinks that the answer to this question is yes. In the video clip below (from the BBC2 Horizon documentary What is Reality? - February 2011), he says, "I think...
counting primes
Even though they do not need to know it for any exam question, I think any student in IB Math HL or SL should be familiar with Euclid's famous proof of the infinitude of primes. The only formal proof...
volume of a donut
One of my students came up with - what I thought - is a good idea for an Exploration: finding the volume of a donut. Or, more precisely, deriving a general formula for the volume of a torus. The torus...
Dealing with Infinity
There comes a time in both Maths HL or Maths SL when probing questions about infinity will be confronted - by both teacher and student - or, at least they should be. This usually first occurs with the...
Remembering Martin Gardner
A few days ago (Tuesday 21 October) marked 100 years since the birth of Martin Gardner, one of the most influential American mathematics and science writers of the 20th century. Gardner was an extraordinarily...
Is infinity a number?
Today I wanted to quickly convince my Maths SL students that for any triangle the ratio of the length of a side to the sine of the angle opposite it is always equal to the ratio of another side of the...
the invention(?) of logarithms 400 years ago
In 1614, the Scottish nobleman, mathematician, scientist and theologian John Napier (1550-1617) published Mirifici Logarithmorum Canonis Descriptio (A Description of the Wonderful Law of Logarithms)....
GDC - visual check ... solution?
Today I posed a fairly common type of 'quadratic functions' question to my first year Maths HL students. The question is also suitable for SL students although questions like this are less common on SL...