(December 10, 2021 at 8:12 pm)brewer Wrote: What's the deal with 3, 6, and 9? (I think it's just about 3 but.........)

3x4=12, 1+2=3
6x24=144, 1+4+4=9
9x2025=18225, 1+8+2+2+5=18, 1+8=9
6x85069=510414, 5+1+0+4+1+4=15, 1+5=6
3x50647921=151943763, 1+5+1+9+4+3+7+6+3=39, 3+9=12, 1+2=3

Nonfunctional math guy is curious.

I'll let polymath257 do the honors for modulo arithmetic.

(December 10, 2021 at 8:12 pm)brewer Wrote: What's the deal with 3, 6, and 9? (I think it's just about 3 but.........)

3x4=12, 1+2=3
6x24=144, 1+4+4=9
9x2025=18225, 1+8+2+2+5=18, 1+8=9
6x85069=510414, 5+1+0+4+1+4=15, 1+5=6
3x50647921=151943763, 1+5+1+9+4+3+7+6+3=39, 3+9=12, 1+2=3

Nonfunctional math guy is curious.

It boils down to the fact that if you divide 10 (the base of our number system) by 3 or 9, the remainder is 1. because of that, when you divide 100 or 10000 or any power of 10 by 3 or 9, the remainder will be 1.

This is actually the basis of a lot of strange arithmetic tidbits.

The effect is that when you divide a number by 3 or 9, the remainder will be the same as what you get if you divide the sum of the digits by 3 or 9. You can keep doing this until you have a single digit number.

So, if you start out with a multiple of 3, the final, single digit has to be 3, 6, or 9.

If you start out with a multiple of 9, the single digit has to be 9.

Here is a variant, that is due to the fact that 10 is the same as -1 when you divide by 11.

Take any multiple of 11 and alternately add and subtract its digits. Than do the same with the answer. Eventually, you will get to 0.

Example:

11x5971=65681. 6-5+6-8+8-1=11, 1-1=0.

11x821074=9031814, 9-0+3-1+8-1+4=22, 2-2=0

Math lobe hurts now.

I math every day as a bookkeeper but Algebra and beyond are beyond what my brain can process.

Most people do basic algebra every day and are blissfully unaware of it. I had a friend who swore she couldn't do it until I asked her what she thought she was doing every time she did a cost estimate for a client based on the dimensions of the project. I wouldn't want to write out formally what she was doing in her head.

(December 15, 2021 at 11:55 pm)Paleophyte Wrote: Most people do basic algebra every day and are blissfully unaware of it. I had a friend who swore she couldn't do it until I asked her what she thought she was doing every time she did a cost estimate for a client based on the dimensions of the project. I wouldn't want to write out formally what she was doing in her head.

Algebra is just arithmetic with letters.

What has been your greatest personal challenge in this field? And greatest personal achievement.

At work.

(December 8, 2021 at 10:27 pm)polymath257 Wrote: I've been a research mathematician for the last 35 years. Any questions?

During your research havd found out if putting racing stripes on the numbers helps counting them go faster?

Have you tried painting them red?

XD

(January 2, 2022 at 12:45 pm)GrandizerII Wrote: What has been your greatest personal challenge in this field? And greatest personal achievement.

Biggest personal challenge: that I am not as intelligent and creative as I would like to be.

Greatest personal achievement: applying algebraic topology to a question in measure theory. The two subjects are quite far apart and to find a connection was quite a trip.

(January 2, 2022 at 3:15 pm)polymath257 Wrote:

(January 2, 2022 at 12:45 pm)GrandizerII Wrote: What has been your greatest personal challenge in this field? And greatest personal achievement.

Biggest personal challenge: that I am not as intelligent and creative as I would like to be.

Greatest personal achievement: applying algebraic topology to a question in measure theory. The two subjects are quite far apart and to find a connection was quite a trip.

As an undergraduate, I had a love (and still do) of mathematics & physics, and had contemplated going to graduate school, but, (somewhat) sadly was forced to conclude that my principle (and, likely, only) accomplishment as a graduate student would have been to have made the top half of my graduating class possible.

And, so, after graduating, I went into industry and bought a car, a Z24.