Favorite Formulae

New to me. Where did you pick these up?

Scott Zelenak, post: 331671, member: 327 wrote: R = abc/SQRT (2a²b² + 2b²c² + 2c²a² - a⁴ - b⁴ - c⁴)
Where, a b, and c are the inverse lengths between the points.

And the radius point coordinates are solved for by;

Xrp=(ya²+xa²-yc²-xc²-(ya-yc)*(ya²+xa²-yb²-xb²)/(ya-yb))/2/(xa-xc-(ya-yc)*(xa-xb)/(ya-yb))
Yrp=(ya²+xa²-yb²-xb²-2*Xrp*(xa-xb))/(ya-yb)/2
Where, xa, ya, etc., are the east and north coordinates, respectively, of the points on the curve.

I've never penciled my way through those, but they look familiar. I believe when purchasing a new 41 (or maybe even a 48) HP offered the "big book" for an additional few dollars. This book was full of the trigonometric formulae that were programmed into the unit for their quickie solutions. These look extremely suspect of the values in HP's little bible. I've got one somewhere here, but can't get my mitts on it right now.

Now for an exercise in practical application of the Pythagorean Theorem sketch and derive the given formulas justifying each step using a known mathematical axiom or property.

That first one looks like it is related to the "semi-perimeter" method for determining the area of a triangle. Perhaps I'm mistaken.

I've never used these, but I love deriving formulae. I might spend some time today working through the process to establish these formulae. Could be fun. Then again, I might just get my work done...

I thought you were going to ask us what our favorite formula was.

I like tanAtanBtanC=tanA+tanB+tanC.

James Fleming, post: 331676, member: 136 wrote:

5 Gin
1 Vermouth
Olives
🙂

Dr Gimlet made the 1912 New Year Honors List for devising a formulae to encourage lime juice consumption by British Naval Officers.
It should only be consumed when math is not occurring.:drink:

Scott Zelenak, post: 331671, member: 327 wrote: Back in the last century, when handheld calculators were the newest technology, I had three formulae I used to solve for the radius point coordinates and the radius length of as-built curves.

Given three coordinated points on a curve, the radius length is determined by;

R = abc/SQRT (2a²b² + 2b²c² + 2c²a² - a⁴ - b⁴ - c⁴)
Where, a b, and c are the inverse lengths between the points.

And the radius point coordinates are solved for by;

Xrp=(ya²+xa²-yc²-xc²-(ya-yc)*(ya²+xa²-yb²-xb²)/(ya-yb))/2/(xa-xc-(ya-yc)*(xa-xb)/(ya-yb))
Yrp=(ya²+xa²-yb²-xb²-2*Xrp*(xa-xb))/(ya-yb)/2
Where, xa, ya, etc., are the east and north coordinates, respectively, of the points on the curve.

Those three formulae were priceless in the field and in all my years of surveying, I've never met anyone who knew them.

Nerd

Dave Karoly, post: 331790, member: 94 wrote: 5 Gin
1 Vermouth
Olives
🙂

I am the heathen that uses:

4 vodka
1/2 olive juice
shake it like you're trying to make it explode
serve in a chilled glass with several olives

Just don't do this while camping... and drinking scotch... and high ABV beer...

skwyd, post: 331973, member: 6874 wrote: I am the heathen that uses:

4 vodka
1/2 olive juice
shake it like you're trying to make it explode
serve in a chilled glass with several olives

Just don't do this while camping... and drinking scotch... and high ABV beer...

When using vodka I shake it too.

My good gin, no way, stirred, always stirred and strained into the cocktail glass.

I use good vodka. For some reason vodka works better shaken but shaking gin just kills the flavor.

These type formulas I love finding them.
Never seen it before. Wish there was a library of these "complete solutions".
So many textbooks and magazine articles get all engrossed in using the fancy formatting and non-sense variable styles.
I think it's to massage the author's ego not help someone enter and use the formulas.
I entered the formula in my HP Prime in a few minutes.
Made some sample problems.
Worked great. Clockwise, CounterClockwise, different quadrants.
Did not try arc over 180 yet.

Gee, if you have any more of these, please share.

Thanks

I've often wondered how CAD software solves the various geometric relationships it has to address. Do they have a way of generalizing these solutions, or did the coders have to set up an algorithm that steps through a criteria analysis to determine which formula to apply in a given situation? Because it happens in what appears to be real time, I usually take for granted what must be going on under the hood.

Two of my favorites have nothing to do with surveying.

HP = 2*pi *R*F*N all divided by 33000. That's the magic formula to determine the horsepower achieved by a certain force applied to a certain lever arm at a certain rate when the units of each comply with the units of the magic formula.

IKLSKP----- each letter corresponds to a specific component of how much water will run off of a specific piece of land in a certain period of time based on rainfall intensity, land slope, soil characteristics, plants or other cover material that impedes flow plus a couple of magic coefficients that come from a table of empirical results from countless studies. Once again, units must conform to a set rule.

Thanks, Radar! It's been gone too long.

Dave Karoly, post: 331983, member: 94 wrote: When using vodka I shake it too.

My good gin, no way, stirred, always stirred and strained into the cocktail glass.

I use good vodka. For some reason vodka works better shaken but shaking gin just kills the flavor.

I'm not a big fan of gin. But I can understand why someone would enjoy a GOOD gin drink.

Jim Frame, post: 332055, member: 10 wrote: I've often wondered how CAD software solves the various geometric relationships it has to address. Do they have a way of generalizing these solutions, or did the coders have to set up an algorithm that steps through a criteria analysis to determine which formula to apply in a given situation? Because it happens in what appears to be real time, I usually take for granted what must be going on under the hood.

I've noticed a quirk in my current version of Civil3D when I'm running map closures. Whenever I have a curve with a delta of 180 degrees, in the closure, it lists the delta as "infinite". It still gives me a correct length and radial bearings and whatnot. But that delta is a bit irritating to see in the reports.

RADAR, post: 332087, member: 413 wrote:

Looks like we need a spiral curve formula for the bun shown in the background. 🙂