Amazing project!

I've been following your postings for quite a while and I must say that your approach to math teaching is fascinating. I would like to have learned in a similar way (not necessarily with model railroad), I enjoy reading the way you incorporate math in a context instead of a theory in which the students may or may not see any real world application. I really look forward to see all your future classes!!

Congrats!!

Daniel Kramer

Math? .... a lazy man's solution .....

http://www.radiustrack.com/curved-right-custom-framing/radius-calculator

lazy vs. resourceful

That's a cool site, I've never seen an entire site devoted to curves! 

It reminds me of what happened a few years ago when I gave my high school math class an assignment to figure out how far away the horizon is. The geometry is closely related to the radius problem above. About half a dozen students brought in almost identical hand-drawn diagrams, which were all based on one that comes up when you google "how far away is the horizon?"!

Jeff Allen

We’ll review your solutions tomorrow.

divide x by 2 then use x/2sq + ysq=sq rt of c(chord). solve for 1/2 delta angle (y /x/2 =tan 1/2delta) then C =2R X sin1/2Delta.or 2R=C/sin 1/2delta.   Example: if y=1, and x=5 then  x/2=2.5, 1sq+2.5sq=7.25, sqrt of 7.25=2.6926=C   1/2.5=.40=tan of 21.8014 deg., sin of 21.8014=.3714.   , 2.6926=2r X .3714, 2R=2.6926/.3714=7.2499/2=R=3.6249..   check =sin D/2= .3714XR(3.6249)X2= 2.6926=C  Whew, haven't done that for about 30 years :> ) ....DaveB

Nice! Very railroady!

DaveB, go to the head of the class! (I'll overlook the small brain fart in the first expression, should be "=square of c").

Although I have introduced trigonometric ratios to some of the students, I've been emphasizing methods that don't require trig since not everyone is acquainted with it yet. However, this year I'll be showing them how curves are actually laid out in the field using degree of curvature rather than the radius, and your method is appropriate for that. 

I was a chainman back in the day and have an old transit that never fails to astonish the kids ("OMG, you can measure angles smaller than one degree!").

Jeff Allen

"I was a chainman back in the

"I was a chainman back in the day and have an old transit that never fails to astonish the kids ("OMG, you can measure angles smaller than one degree!").'

Hi Jeff, Keep up the good work.   I used some of those vernier transits  in the old days to retrace old surveys done with the compass on them. When I first started surveying we had to use books of functions and do the math by hand or with a curta. After a while HP came out with hand held calculators that had the functions then eventually they had cogo and programs which saved a lot of work but made me forget a lot of trig :> )  When I retired we were using total stations and GPS and letting the machines do all the calcs.   The funny thing to me is that it's still hard to find a cheap cogo program for PC or a cogo calculator for home use despite all the years of advancement in software and hardware....DaveB 

Too funny!

When I was in my senior year of college I was one credit hour short so I took a class entitled "Use of a Slide Rule".  All of the other students in the class were football players.  I used my father's slide rule (which I still have and treasure) for the course and was amused to see that when test grades (for others) were passed back most were "Fs".  The amazing thing is that all of the football players passed the course!  When was this?  Well, I also took a course in Fortran 4 and IBM 360!  We spent an entire semester punching out punch cards to figure the average temperature for a month and could even print out a "picture" of the Statue of Liberty with "Xs" on a dot matrix printer!!!

DataCAD LT cogo

CAD program that includes cogo:  DataCAD LT.

I've been using DataCAD for almost 30 years, and since I don't do any 3D, I've been using their lite version (LT) the last few years, because it's cheap.  $295.  I even used the cogo features to verify that a local surveyor's Total Station was giving errant results (though he swore at me).   It saved the developer from constructing a foundation too close to a property line on a hill.

http://www.datacad.com/cgi-bin/commerce.cgi?display=home

I think I've remembered the geometry

DaveB's equality was my clue: sin(delta/2) = C / 2R

It led me to extend line Y thru the center of the circle a distance of 2R, then draw a line from that point to the intersection of x with the chord to form a right angle with C. There are now two similar triangles, with two expressions for sin(delta/2) = Y / C  =  C / 2R.

So R = Csq / 2Y = (Ysq + [x/2]sq) / 2Y

    which can be solved just by geometric construction and pythagoras' theorem. Is this how the middle schoolers do it? 

I'm not sure why this is fun, imperfectly recalling lessons of 50+ years ago, but there must be something really important that I'm postponing.

Thank you for a pleasant distraction.

jolS

" I even used the cogo

" I even used the cogo features to verify that a local surveyor's Total Station was giving errant results (though he swore at me).   It saved the developer from constructing a foundation too close to a property line on a hill.'

 LOL , I'd loved to listened in on that conversation. I've never seen a total station cause  errant results, they either work right or they don't work at all. I have seen surveyors make them spit out errant results though. The smartening up of the equipment has caused employers to think they can hire less experienced  people( for less money)  to run it.  Advanced equipment can't help one recognize a witness scar on a tree or know where the old crew was likely to have set their points along the line so they often end up trying to make measurements fit precisely when they shouldn't ,then they come to a correct corner and think it's wrong :> )        I was thinking more in terms of a $5 app for cogo on a phone or Ipad, seems like it's a less complicated program than Angry Birds? ....DaveB

 "but there must be something

"but there must be something really important that I'm postponing.'

Haha, Nailed it !!   my wife wants me to go to the store :> )