Suppose you have N people and one cake. How can you cut the cake such that each person is satisfied that the pieces have been distributed fairly? This is an old problem that Martin Gardner wrote up in his column for Scientific American and in the case of two people it is quite simple: One person gets to cut the cake into two and the other person gets to select the piece they want. (But see later for a problem with this.)

But what if there are more than two people? Below the fold, I give Gardner’s explanation on how to do it, starting with the case where N=3, quoted by Walter Stromquist in an issue of The American Mathematical Monthly.
[Read more…]

Via Mark Frauenfelder, I came across this fascinating little video that informs me that being in possession of a particular number is now illegal in the US and why. I cannot tell you the full number because I don’t know it but apparently knowing it and even writing it on a piece of paper could land me in prison. All I know is that the number is a prime number that has 1419 digits that begin with the sequence 85650789657397829.
[Read more…]

There are a total of 49 terrible wildfires currently blazing away in Alberta, Canada. While fortunately there have been no deaths and injuries, the damage has been extensive. This news report begins by describing the extent of the fire.
[Read more…]

The sudden and unexpected death of Prince at the young age of 57 naturally arouses curiousity as to the cause. Although he was a Jehovah’s Witness and reportedly abstained entirely from recreational drugs and alcohol, the fact that he was part of the popular music world immediately fueled speculation that drugs were involved. He supposedly had prescription painkillers, needed because he refused to have double hip replacement surgery due to the fact that it would require blood transfusions that are prohibited by his religion, and an overdose of these might be a possible cause.
[Read more…]

Albert Einstein and his wife Elsa stopped off in Colombo in 1922 on their way to Japan but the visit did not receive the kind of widespread publicity in the local papers that one would have expected, given how famous he was. True, he had not as yet received the Nobel Prize. A few weeks after his visit, the announcement was made while he was in Japan that he had received his retrospectively for 1921, but he was still an eminent celebrity. I myself was not aware of this visit until a friend of mine recently sent me a link to this article that summarized what Einstein had written in his private notes about the visit and his encounter with a rickshaw, a mode of transport that has disappeared, though I remember seeing them as a child.
[Read more…]

I visit a lot of websites and a lot of them are like my own where there is a paragraph above the fold that indicates what the post is about and, if one is interested enough to read the full post, one has to click on the ‘more’ link. I have noticed more and more people using gifs (those videos that last about a second and repeat endlessly) above the fold.
[Read more…]

Those of us who love algebra (and even those who don’t) are familiar with problems that end up with the command to ‘solve for X’. But why, of all the letters in the alphabet, has X been chosen for this singular honor of representing the unknown, a practice that has extended well beyond algebra? To the extent that any of us thought of this at all, we may have put it down to sheer accident. Someone back in time picked that letter for who knows what reason and it stuck as others followed the practice.
[Read more…]