A Little Math Fun

[ProfessorGAC]

I came up with this a few years ago. When I sub math, kids dig it. I'm sure it's nothing unique, because mathematicians have probably known it for a couple hundred years. But...
Take a number where all the digits are 1.
11^2=121
Two ones in 11. Middle number of the answer is 2.
Then, 111^2=12,321.
3 ones, middle number is three.
To jump to 111,111.
Six ones. Answer is 12,345,654,321
You count up to the number of ones, then back down.
Past 9 digits, there's still a pattern, but it's not as simple as just counting.
If you think this is a fun fact, let me know.

[Jamastiene]

1. I love math fun.

I forget rules for math courses I had to take years ago. I need to practice it more.

I still don't know how to find the angles of my property based on the lengths of the sides. I eyeballed a map of it and ended up with two angles being close to 90 degrees, but still do not know enough surveyor tricks to figure it out and I cannot afford to hire a surveyor to tell me all of the angles.

I want to be able to make a somewhat similar height map in Sketchup, but I want the boundaries of my property to be right. I believe I can estimate the height elevations close enough, but I would really like to be able to just sit down and draw a top down view of my property. I know the elevations go, I think it was 26' feet from opposite corners of the property.

I know all of the sides, in length, but none of the angles. So, I can only "guesstimate" it.

I would not know what to do if I ever got the exact angles so that all of the sides added up just right with the angles and it all connected in Sketchup just right. I could figure the rest out if I only knew the one angle.

I wonder how surveyors do it and what I am missing. I cannot believe something that looks so simple has stumped me this way. I feel like the dumbest person in the world for not being able to solve this problem.

[Ptah]

2. What are the lengths of the sides?

[Jamastiene]

3. 122, 264, 108, and 255

Starting from the road frontage, it is 122, then going counter clockwise, it is 264, then 108 across the back and 255 for the other side of the property.

[Ptah]

4. If I understand your numbers this is what it might look like:

If you can measure either of the red lines,
the angles can easily be determined.

[Jamastiene]

5. Close, here is a screengrab of what it looks like.

[Ptah]

6. I misread the counterclockwise.

If you can measure from corner to corner, the angles are easy to determine.

[eppur_se_muova]

9. Well, it's probably safe to assume the two sides are parallel, since lots are normally surveyed ...

that way. So draw the largest rectangle that can fit between those two parallel sides. You will have two little triangles sticking out at the ends. Now, draw the smallest rectangle that includes the whole property. This will have added twice the area of the two triangles. Average the area of the two rectangles, and that's the area!

Problem is ... you don't really know the width of the rectangle, so you can't find the area. If your frontage is on a curving road, it may be that the frontage is at a slant, but the back edge of your property really is at right angles to the sides, and you could assume the lot is 108' across, measured perpendicular to the sides. The smaller rectangle would then be 108x255, and the larger 108x264 -- so the average is just 108x259.5, or 28026 sq. ft. Of course, the angles in back are not perfect right angles, it will be slightly less, and if the property slopes, the actual area will be somewhat larger, but that gets you an estimate.

[eppur_se_muova]

7. Try going on to cubes and higher powers of 11 -- good intro to Pascal's triangle.

Handy for predicting the patterns of NMR multiplets.

https://socratic.org/questions/what-is-the-pascal-s-triangle

[ProfessorGAC]

8. Yep!

I don't sub kids taking that level of math, so I stay with squares.
How much NMR work did you do?

[eppur_se_muova]

10. A fair amount, but I got out of research just as modern pulse sequences were really taking off.

Mostly, I just did routine structural assignments of synthesis intermediates, none *too* complicated.

{I tried to find a 131Xe(19F) spectrum of Xe(OSF5)4 for this post, but I don't have access to journals. IIRC this was a beautiful example of the 18th row of Pascal's triangle. }

[ProfessorGAC]

11. I Did Mine, Pretty Much In Grad School

When working, I'd give samples to Analytical and they had 2 people doing almost nothing else.
I can still read spectra, but I wouldn't begin to know how to operate the new hardware.
Same is true of MS.
I did a lot of my own FTIR work. There are many fewer technique errors on those. GC & LC I had to do a lot of.
I was developing processes for which there were no methods. I needed the data to develop kinetic models.