August 3rd is watermelon day in Kentucky, so chill one up and crack that sucker open, take a big bite and let the juice run down your cheeks and spit seeds to your hearts content... heck, its almost an obligation today.
The 8/3 reminds me of that first introduction to integral calculus. 8/3 is the area under the simple curve y=x^2 from zero to two, perhaps the first integral I ever did, somehow it still seems impressive in spite of the fact that Archimedes could do it 200 years before the birth of Christ. He did it using pricinpals of levers thus carefully avoiding all those epsilon-delta proofs.
Speaking of caluculus, this is the anniversary of the death of Ferdinand Georg Frobenius, who proveded some important theorems in differential equations, Eigen vectors and all those cool things. He died in 1917.
It is also the birthday of the guy who made skyscrapers possible, Elisha Graves Otis. If the name sounds familiar and you can't place it, you may have seen it on the Elevator you rode last. Some people even think he invented the elevator, but he actually only invented a safety break to keep them from falling. Otis introduced his new device with a bit of showmanship at New Yorks Crystal Palace by ordering a workman to cut the only rope supporting the platform on which he stood. The platform dropped a few inches, the crowd went "ooohhhhh" and the Otis Safety Elevator company was born. According to the people at United Technologies, which is now the parent company, the number of people who ride an Otis elevator in a nine day period equals the population of the world.
On this day in 1900, John T Scopes was born, defendent in the famous "Monkey" trial. Hard to believe that people are still getting fired for teaching evolution.
The Noble Prize Economist, Bertil Ohlin died on this day in 1979. He is the guy who came up with the mathematical theory that explains that if a country can make both guns and butter, it will have a competitive advantage on the product that uses domestic resources rather than imported ones. It's called the the Hecksher-Ohlin model for those who wish to explore more. (OK, I'm not an economist, so if one of you wants to correct the flaw in that simple explanation, send a clear succint note, without obscenities please.)
August 3 is the 215 day of the year, so that leaves 150 to go. I really couldn't think of anything super exciting about 215, but in case I don't write tomorrow, 216 is the smallest cube that is the sum of three cubes of positive integers... 216 = 6^3 = 3^3 + 4^3 + 5^3 ...
To me that is sort of an extension of the Pythagorean 3-4-5 identity, since the numbers all occur in sequence.... ie
3^2 + 4^2 = 5^2 and
3^3 + 4^3 + 5^3 = 6^3 Now I know you are thinking, "Can it be?" and alas the answer is no... but quickly now, what is the next cube that is the sum of three cubes?
Look way below for one answer
\
\
\
\
\
1^3 + 6^3 + 8^3 = 9^3
