Forget Trig as we Know it!

Great article, thanks for posting it!

[USER=7674]@MathTeacher[/USER]

Could you elaborate on this for us morons in PLSSia. 😉

"However unlike todayƒ??s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate."

Ya'll Texans probably already know. So keep quiet. 😉

I decided to go ahead and forget all the trig I knew a while back:cool:

FL/GA PLS., post: 443208, member: 379 wrote: Great article, thanks for posting it!

[USER=7674]@MathTeacher[/USER]

Could you elaborate on this for us morons in PLSSia. 😉

"However unlike todayƒ??s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate."

Ya'll Texans probably already know. So keep quiet. 😉

I guess you guys in the PLSS will have to wait till they make a new discovery on how to draw a square.

FL/GA PLS., post: 443208, member: 379 wrote: base 60, or sexagesimal system

So, now that I'm 60; does that mean I have to guess at what sex was like?

paden cash, post: 443081, member: 20 wrote: (head explosion)

I will be taking bets on how fast this country moves to a "far simpler system". I've already got dibs on "Never" and "No Way".

FL/GA PLS., post: 443208, member: 379 wrote: Great article, thanks for posting it!

[USER=7674]@MathTeacher[/USER]

Could you elaborate on this for us morons in PLSSia. 😉

"However unlike todayƒ??s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate."

Ya'll Texans probably already know. So keep quiet. 😉

lol. For the record, I don't think that any surveyor, whether in PLSSia or METESia, is a moron. Your profession requires a unique combination of intelligence, knowledge, and physical ability that pretty much denies long-term survival to morons.

Writing numbers using any base, whether it is the base 2 that computers use, the base 10 that we commonly use, or the base 60 that the Babylonians used, relies on place values and exponents. When we write the number 5280, for example, the 5 occupies the thousands place (10^3), the 2 occupies the hundreds place (10^2), the 8 occupies the tens place (10^1) and the 0 occupies the units place (10^0). So, the number is 5 x 10^3 + 2 x 10^2 + 8 x 10^1 + 0 x 10^0.

That same number, 5280, written in base 2 is 1010010100000. That means 1 x 2^12 + 0 x 2^11 +1 x 2^10 + 0 x 2^9 + 0 x 2^8 + 1 x 2^7 + 0 x 2^6 +1 x 2^5 +0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0. Instead of representing numbers as sums of products of powers of 10, base 2 represents numbers as sums of products of powers of 2.

Note that base 10 needs 10 symbols (0,1,2,3,4,5,6,7,8,9) while base 2 needs only 2 symbols (0, 1). But base 2 requires longer strings to represent most numbers.

Base 60 represents numbers in powers of 60 and requires 60 symbols. Typically, base 16 numbers use the symbols 1,2,3,4,5,6,7,8,9, A,B,C,D,E,F. Base 60 needs many more.

Using the scheme for representing base 60 numbers on this calculator, http://www.dcode.fr/base-n-convert 5280 in base 10 is 1s0 in base 60. Note that it requires fewer digits than base 10.

To me, it's debatable whether the gain from representing more fractions more exactly is worth the overhead of 60 symbols, but the Babylonians seem to have been comfortable with it.

Not all mathematics historians are convinced that the interpretation of the tablet as trig is correct. That's understandable when an old idea is challenged, but that's something that the intellectuals will have to debate.

Knowing the roots of mathematical processes is important, but declaring absolute superiority of one method over another without considering context is, I think, a bit presumptuous. I'm set in newer ways!

Ruel, that was awesome!

John, post: 443224, member: 791 wrote: I will be taking bets on how fast this country moves to a "far simpler system". I've already got dibs on "Never" and "No Way".

Great, you copyright them and I'll copyright "it depends". 😉

A bit of a hijack - here are two great reads for all you math geeks:

John, post: 443224, member: 791 wrote: I will be taking bets on how fast this country moves to a "far simpler system". I've already got dibs on "Never" and "No Way".

I'll put my 4 bits on the "When Donkeys Fly" square.

John, post: 443224, member: 791 wrote: I will be taking bets on how fast this country moves to a "far simpler system". I've already got dibs on "Never" and "No Way".

We've already rejected the Metric System (at least as far as the populous goes) so I can't even imagine what that would do.
Andy

Scott Ellis, post: 443211, member: 7154 wrote: I guess you guys in the PLSS will have to wait till they make a new discovery on how to draw a square.

WOW
You really went there.

Now I will return to working on a metes and bounds plan with record deeds missing courses and calling for stakes from 100+ years ago near the edge of a swamp turned active cranberry bog. And of course, none of the parcels are square.

MathTeacher, post: 443228, member: 7674 wrote: Knowing the roots of mathematical processes is important, but declaring absolute superiority of one method over another without considering context is, I think, a bit presumptuous. I'm set in newer ways!

Amen, brother...

I remember a lesson in 6th grade math: The teacher asked, what if we had 6 fingers on each hand? Then proceeded to show us how a base 12 system would work...

Anyone who has ever had a TI-83 calculator inflicted upon him or her will definitely think some reform in the area of math education and base 60 is in order. One method for entering degrees and minutes, a different method for entering seconds? Really?

I know a dumb guy who got arrested for counting in public to twenty-one on his fingers, toes...

ashton, post: 443306, member: 422 wrote: Anyone who has ever had a TI-83 calculator inflicted upon him or her will definitely think some reform in the area of math education and base 60 is in order. One method for entering degrees and minutes, a different method for entering seconds? Really?

It is clumsy to say the least. On the TI 89, it's still somewhat clumsy, but consistent. My big problem with the 83/84 is that they round seconds to 3 decimal places. The 89 does not, so it's usable for geodetic work.

Math Teacher nice post above on different base systems.

JOHN NOLTON

Scott Ellis, post: 443211, member: 7154 wrote: I guess you guys in the PLSS will have to wait till they make a new discovery on how to draw a square.

Nah, us PLSSian's are just waiting for ya'll "Texans" to screw everything up so bad that the PLSS system will be instituted by the GLO. 😉

spledeus, post: 443249, member: 3579 wrote: WOW
You really went there.

Now I will return to working on a metes and bounds plan with record deeds missing courses and calling for stakes from 100+ years ago near the edge of a swamp turned active cranberry bog. And of course, none of the parcels are square.

If the PLSS Surveyors want to keep bringing up how hard the Surveying in Texas is, I will keep reminding them how easy it is in PLSS