A way to multiply
- Do you want to hear about my latest invention?
- Do I have a choice?
- It is an easy way to multiply numbers.
- You mean, reaching for a calculator?
- Let’s say you want to multiply 2 by 3.
- I want that all the time.
- Join the points (-2, 4) and (3,9).
- Where did those points come from?
- They are (-a, a2) and (b, b2).
- OK.
- Where does the line you drew intersect the y-axis?
- Amazing! Does it always work?
Source: Wild about math.
November 30th, 2007 at 1:17 am
Neat, and yes it’ll always work.
slope = rise / run = (b²-a²)/(b+a)
So from the point (-a,a²) to the y-intercept, is theoretically:
a(b²-a²)/(b+a) + a² = ab
If the above is true, the sides should be able to be shown as equal. Here ’tis:
(b²-a²)/(b+a) + a = b
(b²-a²)/(b+a) + a(b+a)/(b+a) = b
[(b²-a²)+(ab+a²)]/(b+a) = b
(b²-a²)+(ab+a²) = (b+a)b
b²-a²+a²+ab = b²+ab
b²+ab = b²+ab
November 30th, 2007 at 6:03 am
*sigh* I was actually able to figure that one out. No wonder i never get laid…
December 3rd, 2007 at 12:03 am
[...] Richard Sabey has kindly submitted this dialogue as a reaction to the post A way to multiply. [...]
October 12th, 2009 at 7:20 am
It would be easier to multiply 2 by 3