Is the NYTimes' mathematician blogger (yes they have one) a bit out of touch? Here he is reveling in the thought that, if the material is presented in a certain way, a 2nd grader could perform certain basic principles of calculus.
If you are at all familiar with calculus, you may know that the vertical velocity is the first derivative of the height, and the acceleration is the second. If you didn’t, don’t worry about it: the simple procedure for second graders that we just did will give us the answers. They are as follows:Um, yeah. Note the error that had to be corrected. But also, subtracting negative numbers? Variables? Do kids even divide double-digit numbers in half in 2nd grade, let alone negative numbers?
1. The gravitational acceleration (g) at the planetoid surface is the number in the last row. This comes out to be -14 meters/sec/sec.(Error corrected) (The minus sign indicates that it is downward in direction). For future reference, remember half this number (-7).
2. The vertical velocity of the cannonball is the first number in the second row minus half the g that we just determined. It is therefore 28 – (-7) = 35 meters/sec.
3. The vertical height of the cannon (obviously) is the first number in the first row. That’s 20 meters.
Now look what else we’ve accomplished! Given a sequence of numbers, we have, easy as pie, found the polynomial formula for it: it is the sum of the three numbers above: -7x2 + 35x +20. You can substitute the numbers 0 through 5 for x and confirm that you get the original series.
Easily done, using simple arithmetic that a second grader could do!