doodle schooled

my mom always said, no matter how good you are at something, there will always be somebody else who will be better than you are.

and so, i present the "why" of math doodling, courtesy of the triumvirate of smarty pants in my personal orbit.

Its a symbol of the multiplication you have to do to arrive at the final answer. There is really nothing to the graph itself. For instance write out the problem the traditional way:

X 12

the steps you need to take are:

2X2 (symbolized by the upper right)
2X4 (upper left)
2X1 (lower right)
4X1 (lower left)

if you do the multiplication out longhand you'll see the way the are put together- when you do the 2X2 that is the right side of the answer, the 4X1 is the left side. But you have to add those middle 2 up (the 2X1 and 2X4) which is why the middle of the diagram is added. and the 1 is carried to the left side of the equation, just like in the long hand method.

If you reversed the order in which you draw the multiplication factors (i.e the 2 starting on the top, instead on the 2 on the bottom), your just reversing the order in which you are multiplying, getting the answer to 42 X 21.

i also think it works because when you multiply, you are just dealing with 1's which can be represented by simple tick marks. the process of multiplying you learn in grammer school is all about breaking a problem of multiplying 10s and 100s into the simple task of just multiplying with 1's, and then adding them up to get the 10s and 100s. This all goes back to binary theory!

sadist jane:
Hey, I did this with 42 x 23 and got 966.

So did Matlab. I am matlab.

That's logic, not math.

*** but really ***

Do you know how an abacus works? this is a similar accounting system - it's a means of keeping track of the digits (in powers of ten) - then the intersections are the products. The problem is you have to be moving in the same direction on the 90 degree plane, so it's not very intuitive (i.e. the 10s columns in our numbers don't both go at the 'top', they go at the 'left' in their respective orientation).

OR, you can think of the numbers as sort of in a matrix, and you're doing inner and outer products. It's not as though the lines help with the accounting once the entry exceeds 9.

the flyshower:
this is basically a variation on lattice multiplication, which is basically the same general 2D format but with numbers. i'll show you sometime. yhat's pretty dope though thanks for sharing. sharing is caring, you know.

so if nothing else - i do care. really.


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