4+ hour, 7+ min ago  (399+ words) Yesterday I wrote a post showing that the trapezoid rule evaluates the integral very efficiently. But how do we know what the exact integral is for comparison? If you ask Mathematica, it will tell you the integral equals "2" J1(1) where J1 is…...

4+ mon, 4+ week ago  (372+ words) Here's something I've wondered about before: are there good mnemonics for chemical element symbols? Some element symbols are based on Latin or German names and seem arbitrary to English speakers, such as K (kalium) for potassium or Fe (ferrum) for…...

5+ mon, 1+ week ago  (749+ words) One of my daughters gave me a Klein bottle for Christmas. But is a Klein bottle real? My Christmas present is a real physical object, so it's real in that sense. Is a Klein bottle real as a mathematical object?...