When can YOU do this? Under what circumstances can you multiply swiftly? Do you ever make a (let us all pause here) geometric illustration of your calculation in your head? Can you picture something with, say, algebra tiles? Let me illustrate.
Let the following illustration of a rectangle represent the product of 43 and 42. Let the horizontal represent 40+3 and the vertical represent 40+2. The blue square represents 40x40; the green bars each have dimension 1 x 40; the yellow squares each represent a 1 x 1 unit.
...or how the tiles support FOILing:
But there's more. I'd like to draw your attention to two modern-day mathematical geniuses from India.
One woman, Shakuntala Devi is known as "The Human Calculator" for her ability to calculate products of large numbers in her head very swiftly. From the on-line version of the India Times:
Shakuntala Devi once competed against a computer to see who could come up with the cube root of a 9 digit number first and she defeated the computer at this challenge. The same year, in 1977, Shakuntala Devi was asked to give the 23rd root of a 201-digit number; she answered in 50 seconds! On June 18, 1980, she demonstrated the multiplication of two 13-digit numbers 7,686,369,774,870 × 2,465,099,745,779 picked at random by the Computer Department of Imperial College. The correct answer was presented by her in just 28 seconds!
I've always loved stories of Srinivasa Ramanujan. One of my favorite stories is the following, from Durango Bill's site:
If you mention the number “1729” or the phrase “Taxicab Problem” to any mathematician, it will immediately bring up the subject of the self-taught Indian mathematical genius Srinivasa Ramanujan. When Ramanujan was dying of tuberculosis in a hospital, G. H. Hardy would frequently visit him. It was on one of these visits that the following occurred according to C. P. Snow.
“Hardy used to visit him, as he lay dying in hospital at Putney. It was on one of those visits that there happened the incident of the taxicab number. Hardy had gone out to Putney by taxi, as usual his chosen method of conveyance. He went into the room where Ramanujan was lying. Hardy, always inept about introducing a conversation, said, probably without a greeting, and certainly as his first remark: ‘I thought the number of my taxicab was 1729. It seemed to me rather a dull number.’ To which Ramanujan replied: ‘No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.’”
A second option for your blog this time is to search the web for yet another "human calculator." Have your mathematician be from relatively modern times (the last 100 years) and write something about him or her. Include your internet sources in your blog.
A third option for your blog this time is to find an interesting story about one of these two folks that I identified above that are NOT on the sites I've provided for you. Also be sure to include your internet sources in your blog.
