I had great high school math & science teachers as well. It was the late 70's, no calculators allowed until one could show they were able to solve problems by hand, again and again. Wonder if it still works that way?

Looking at that website reminded me of the reason people used to be willing to pay $100 for a calculator that did this for you - in less than a second.

Heck, I took my high school math in the early 1960's before calculators. I remember purchasing my first TI calculator in the early 1970's and being thrilled that I could get logarithms, trig functions, and square roots. I come from the days of using a slide rule. Now, if we could have a bit of instruction on that device. I still have one lurking around in my drawers somewhere.

If you want to learn statistics, I suggest you get hold of the opensource software called "R" (http://cran.r-project.org/). Not only does it do all statistics, but learning how to use R pretty much gives you the understanding of what you're doing. I insist all my students use it to learn basic stats.

What's a 'standard deviation' ? Think about it.

Always have an answer for sigma in each general population you generalize about, and if you don't have, or can't get, the exact answer: Estimate.

So you recognize (to yourself) you are only speaking (opining) from your estimate. ('You' here does NOT mean you, Jack. Unless it does.)

Probability and statistics R my forte. fwiw.

(I carry a slide rule in my astrology Dr's Black Bag -- the real deal -- and two 20-yr-olds saw it last week and had absolutely no idea what it was, even when I said 'slide rule,' they had never heard the term. fwiw.)

Jack, what's a 'cipher'?

(This is a trick question. Naught.)

I can honestly say that, as a child of late 80s-early 90s HS math (and a couple years of college calc), I had NO IDEA how to manually calculate a square root. I simply used trial and error to get close to the right answer if I didn't have a calculator handy. Neat trick!

It works.

Jack, you aren't by chance taking the STAT 4/551 class at PSU on Tuesday and Thursday mornings, are you? Saw somebody who got up to do a problem at the board who might have been you...

The next level of understanding would be to think about this for a while, and work out in one's mind why this system works.

I believe you can get there starting with the Taylor's expansion for y = sqrt(x). But if I go there, I know I won't let it rest until I prove it, and my day is shot. I'm off to play instead.

Wow, that brings back memories.

I remember memorizing times tables and division tables in 3rd and 4th grade in early '50s. In sixth and seventh grade we had to memorize all the squares of numbers from 1 (1) to 25 (625), as part of learning to do square roots.

I also remember in the 80s in Portland, almost every night, lying on the living room floor, no tv, no radio on, teaching my two oldest fractions and decimals because the teachers at Stephenson literally could not teach math even with calculators. And with calculators, the kids learned nothing.

Hmm. Both pof them went on to do fairly well with calculus, Booleian algebra, etc. One went to Wilson and knew more math than any teacher he had. Other to Benson, and had some teachers who actually knew math and how o teach i.Both engineers now.

Sdaly, neither had a chance to ever take geometry. Both "plain" or Euclidian geometry, and solid geometry are fascinating. More art courses than math.

Jack,

When it all goes to hell, you'll be in demand.