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Strictly Surveying

Last Post by mathteacher 1 month ago

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MightyMoe

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SWMBO and I walk in the early morning where we stay while visiting the grandkids. Got to get in some exercise before the chaos happens. The usual walk is a big circle and ends up being close to 5k (3.1 miles). It's along two streets and we walk the inside of the circle so I told SWMBO that we could get extra distance by walking the outside of the circle. I stepped off about 60' from the inside to the outside. So how much do you gain by the extra 60'. Turns out that no matter the radius it is 2piR with R being 60 or 6.28x60=377'. This works out if the radius is 60' or the radius is 10,000' how much more distance do you cover if it's 10,060' 377'. If the original radius is 1' you gain 377' for a 61' radius, so we could circle around the parking lot and get the same result. In fact if it's the earth radius and you add 60' it's the same 377'.

I got to thinking about it and times I've laid out tracks. A 400 meter track with 2 100m straight sides and 2 100m curve sides need lane adjustment for the 200 and 400 meter races. Expand the track to 1600m with 400m sides and how much larger will the lane adjustments end up. The answer is they will be the same as the 400m track. Same if the track is only 40m with 10m sides.

Somehow it doesn't feel correct, but it is. No matter how big the circle is, you don't need to know the radius to figure out how much expanding it adds to the circumference.

Posted : August 20, 2026 7:20 am

MightyMoe

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A quirky math result has to do with palindromes:

The square of 1 is 1 of course.

The square of 11 is 121, a palindrome

The square of 111 is 12321

The square of 1111111 is 1234657654321, a palindrome.

All the way up to nine ones it holds. After 9 it falls apart.

If someone ever wants the square of a series of ones, all you need to do it simply count it out increasing then decreasing and you have the answer.

Posted : August 20, 2026 9:05 am

holy-cow

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That's a bit like challenging someone to give you a number with eight digits and you wil tell them in under five seconds if that number is divisible by 18.

That sounds impressive. It's not. Add the digits to see if the result is nine and then check that the number is even. You can ignore any nine and any simple pair of digits that adds to nine to focus on the remaining numbers.

18273645 is not divisible by 18 because it is odd. Reverse the last two digits to get 18273654. BAM!! That is divisible by 18.

This post was modified 1 month ago by holy-cow

Posted : August 20, 2026 10:00 am

MightyMoe

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To find if a number is divisible by three quickly add the integers and if the answer is divisible by three then the entire number is, you can eliminate any integer that is divisible by 3 plus 0 and you can eliminate any two that add up to a divisible number. So 6247089 is divisible by three, cross off the 0, 6 and 9, 2+4 is 6 so the 2 and 4 are gone, 7+8 is 15 so they are gone leaving you with a number divisible by three.

Posted : August 20, 2026 10:28 am

holy-cow

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@mightymoe Use the same process to see if it's divisible by 9. If it is and an even number, it's divisible by 18. In your case, find if the digits add to 3, then if it is an even number it is also divisible by 6.

The 60 minutes in an hour can be divided evenly by 1,2,3,4,5,6,10, 12, 15, 20, 30 and 60. How convenient is that? The degrees in a circle are divisible by 360, 180, 120, 90, 72, 45, 40, 36, 24, 18 and 9 plus the same list as for 60.

Posted : August 20, 2026 11:03 am