The article in question makes the point that it is not enough to make easy things easy and hard things possible. It is also necessary to make trivial things trivial. This is a very nice observation, and one that, in his own way, Arnold Bennett expressed in his book ‘How to live on 24 hours … Continue reading article on computer programming →

Here is the link to the Wikipedia article on this topic. The construction is possible up to, and including, 7824. That is, the first breaking point, or failure point, is 7825. keywords: [Pythagoras] [Mathematics] [partition] [sum of squares [hypotenuse] [legs of a triangle] [coloring, in the mathematical sense]

(suggested new terminology) Definition. The lunar eclipse of a 4-digit number (padded with leading zeros, if necessary) is the result of creating the largest number possible from the digits of the number and creating the smallest number possible from the digits of the number and then subtracting the smaller number from the larger number. For … Continue reading the lunar eclipse of a number →

Definition. (suggested new terminology) A set of natural numbers is said to be of critical mass fif there exist arbitrarily-large sets of natural numbers, all of whose sums belong to it. Theorem. (Folkman’s theorem) Every finite partition of the set of natural numbers contains a member of critical mass. Here is the link to the … Continue reading Folkman’s theorem →

Here’s the link to the May Clinic article on this topic. keywords: [blood clot] [pulmonary embolism] [human physiology] [pathology] [lack of exercise]

Here’s the link. keywords: [Mathematics] [Number Theory] [Euler’s totient function] [Euler’s φ function]

Here’s the link to the Wikipedia article on this topic. keywords: [Mathematics] [Number Theory] [Euler’s totient function] [Euler’s φ function]