#8

I see some sort of pattern but I'm not exactly sure how to attack it and prove.

I see that a(1)*b(1) = 100-4/4

then for the second a*2+1 * b*3= 625-1/4

I'm not sure about my thinking. help please!

How about this?

a x b = ((a+b)^2 - (a-b)^2)/4

See the pattern?

The pattern I'm seeing first off is:

a x b = [(a + b)squared - (a - b) squared]/4

I haven't tried to prove it past that.

But note how 13 +12 = 25 and 25 squared = 625. The other two behave similarly. Now I'll work on it further. This is one of those puzzles that's entertaining but one wonders what value there is to it. Beyond mental calisthenics, anyway.

Edit: I think that might be it. It multiplies out OK.

__________________
1986 300SDL, 362K
1984 300D, 138K

CMAC=plumber with a Math degree.

__________________
You don't need a weatherman to know which way the wind blows - Robert A. Zimmerman

Hint: start the proof by expanding ((a+b)^2 - (a-b)^2)/4 and see what cancels out.

if I expand it out I think I get (2b^2)/4 = a*b

but that doesn't work out properly.

I suck at proofs.. this is my second time taking this class(well first I'm taking the lower level discrete course )

Try this:

(a+b)^2 = a^2+2ab+b^2

(a-b)^2 = a^2-2ab+b^2

so,

((a+b)^2 - (a-b)^2)/4 = 4ab/4 = ab

It's been awhile, but I think that's correct.

ahhh I see where 4ab comes from now.. ok

Yes dear friends, stay in school, don't go down the primrose path to blue collar anonymity as I have, only to see your talents squandered on installing toilets that don't leak poopy smelling water out onto the floor.

Actually, one plan is to finally get that math degree (about 2 years left) - trouble is, teachers are projected to be in serious demand around the time I'm in the 65 to 70 age range. But, teaching would probably be easier on the body than construction/plumbing at that age.

__________________
1986 300SDL, 362K
1984 300D, 138K

Here I went and did some work and missed all the fun.

Now if I knew the difference between -> & <-> in (6b) the logical statement I'd really be ready to have fun.

I try to use my mind and the past year of chemo & 5-a-day opiates is still very present. I sure hope that diminishes.

Good math teachers are always in demand.

__________________
1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13

It's disturbing how much I have lost of my mathematical skills. It wasn't until I looked at those problems that I realized how much static I have within. Very disturbing. It reminded me of what it was like after being out in the desert with the bag of cactus.

I'll try to take it one step at a time.

My mother keeps telling me that I should look into teaching vocational math. Might be cool, I don't have any pride around teaching blue collar as opposed to scientific math. False modesty aside, I did pretty well with calculus and analytic geometry but have had no opportunity to make use of those exact skills, maybe some mental strength was gained in the process, not sure. If I had become an actuarial or designer of economic models, those items would have been of more value, no doubt.

I've encountered numerous strong young men who wanted to advance in construction and other trades skills but were hampered by their inability to read, add, and subtract fractions, as in, on a tape measure. Metric might be better but let's face it, ain't gonna happen here short of a divine interference.

__________________
1986 300SDL, 362K
1984 300D, 138K

Doing/understanding math is a lot easier than teaching it. I don't think I had any really good college math instructors untill grad school. I may have learned more math in physics and engineering classes than in math classes as an undergrad. I had one very good math teacher for high school calculus.

I was fortunate, had one in jr high.

cmac - applied math to vocational students sounds like a good fit for you.