I wonder if some of the people arguing that the lockdowns to reduce spread of coronavirus should be lifted are being mislead by an instinct that's generally sensible but doesn't apply here, for interesting reasons. To a spherical-cow level of approximation, we have two problems – people dying of coronavirus, and people losing their livelihoods … Continue reading Algorithmic optimisation and opposition to social distancing measures.
“x mod y” is mathematician-speak for “the remainder you're left with when you try to divide x by y” - that is, to work it out you take away as many copies of y from x as you can. Eventually you'll be left with a number smaller than y, and that's x mod y. That's … Continue reading Maths investigations for children at home 4: modular arithmetic
One of the "nice" things about number theory is that it gives rise to some problems that are extremely easy to state and understand, but very hard to prove. Your children won't be able to prove any of these, but they might have fun looking for counter-examples, and they might think it's fun to work … Continue reading Maths investigations for children at home 3: unsolved problems
The Fibbonaci sequence starts 0,1,1,2,3,5,8,13,21...; each term is the sum of the two preceding terms. Using Excel (or another tool if you prefer, but I think Excel will be good for this) work first 40 terms of the sequence (you can do this by entering a formula that says "this cell is the sum of … Continue reading Maths investigations for children at home 2: Fibonacci numbers
Write out a list of all the numbers from 1 to, say, 100 (it may help to put them in a rectangle; depending on the width of the rectangle you may see pretty patterns. Cross out all the multiples of 2, then all the multiples of 3; 4 is crossed out already (by 2) so … Continue reading Maths investigations for children at home 1: Prime factorisation