In 1981 I took the (then) LSIT exam.?ÿ The morning was open book and the afternoon was closed book.?ÿ There was a question on the afternoon session that I did not know the answer to so I had to derive it.?ÿ Afterward I looked up the answer to make sure I had it right and nearly 40 years later that formula is still in my head.
The question: What is the formula for the external of a circular curve?
The answer: t x tan delta/4
Sometimes those problems are the best teachers.
Andy
@bruce-small?ÿ Wow.?ÿ I sat here with my eyes closed trying to come up with a way to spot a shortcut.?ÿ 10 minutes.?ÿ Nothin.?ÿ Finally got my 11C out.
@dave-drahn The angle is very close to one tenth of a radian, which means the triangle is close in shape to a 100 hypotenuse, 10 opposite side and 99.50 base. Divide by 8 to get closer to our triangle, and the difference between the hypotenuse and the base is 0.06, so 12.67 - 0.06 is 12.61. Voila.
Second the tenth of a radian. The arc from the hypotenuse to the base is 1/10 of the hypotenuse and it's virtually the same length as its chord. I used 1 for the hypotenuse, 0.1 for the opposite side, so the base is sqrt(1-0.01) = sqrt(.99) which is approximately half way between 0.99 and 1, or 0.995. Thus the difference between the base and the hypotenuse is 0.005 times the hypotenuse.
You can also get there mentally by knowing that the sine of a small angle is very nearly equal to the angle's radian measure.
I really like the way you did it. Knowing a 100, 10, 99.5 triangle is cool. Thanks for sharing it; I've copied it to my memory.
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I'm pretty sure there is a page in my Lefax "Mathematical Tables" binder listing triangle formulae... Anyone remember Lefax?
I've copied it to my memory.
Unfortunately, these days I only seem to be able to write to my memory with disappearing ink.
I'm in the same boat.?ÿ
Funny thing, I can explicitly remember conversations from 60 years ago, but I can't remember where I set my car keys yesterday evening.?ÿ
Best LSIT question was in the parking lot afterwards.
We were chatting about how we thought we did. And he asked (oddly) ??how many feet in a rod???
(paused on that) I don??t really know.
??really, is it 15 or 16 feet???
(pause again) I don??t know how many feet, but I positive it??s 1/4 chain.
He wasn't too happy with that answer ?ÿ
so, questions about obliques didn??t seem pertinent.?ÿ
My best memory from taking the LS exam:
The exam was given at the office of our State Board for Engineers & Surveyors.?ÿ The PE exam was also given at the same time back then.
There were two doors on the building in which the test was to be administered.?ÿ One was on the north side of the building (nearest the main parking) and the other was on the south side, requiring a walk around the building.?ÿ Both entrances had a small canopy.
The doors opened at 7AM and it was late fall, meaning it was still dark.?ÿ It was pouring rain like a cow pissing on a flat rock and there was a 25 mph wind out of the north. Near 7AM we all began migrating quickly from our cars to the building.?ÿ I chose the covered walk to the south side of the building to stay out of the wind and rain.
As we all huddled waiting for the doors to open we chatted.?ÿ We soon realized all of the people that had chosen the south door were there to take the LS exam.?ÿ Someone reasoned that the door on the north side of the building must be where all the PE participants were located.?ÿ They opened the doors on both sides of the building and we all entered to see signs that directed the LS folks to one room and the PE folks to the other.
We watched as all the soaking wet PE folks filed into their room.?ÿ One astute aspiring surveyor (it wasn't me) noted they all would probably pass their PE exam since they "didn't have the sense to get out of the rain".?ÿ 😉
@bruce-small that is a statement that only a MathTeacher could like.
but I can't remember where I set my car keys yesterday evening.?ÿ
I tend to be systematic about some things. Keys go from ignition to pocket and stay there unless changing clothes when they go to dresser.
Glasses similar rules.
Anything else may have more possibilities.
Me and two others, a classmate and a guy from knowing it all where that showed up went to Houston for a few days at the expense of Houston Lighting and Power to apply for jobs.
The first day we spent half a day taking IQ and other basic understanding tests. Then under the guidance of an absolute sexist human relations dude, a trip to the Petroleum Club for lunch and then back to the company for a tour of their facilities and introductions to whoever happened to stop and ask what we were looking for and a most interesting elevator ride with a couple of resident ladies who were ready to gut the human relations dude before we reached our destination.
The second day was interview time with the VP of the company where we learned that we would be making about half of what was promised up front, 1st offer of $300 a month paid monthly and that we were to be housed with 6 or 8 others in homes the company owned around the city while they hired a draftsman classmate at $900 a month a week prior.
I boldly told the VP in charge that the offer was insulting to my capabilities and said that if he could make it $900 a month, then I was theirs. He countered with his final offer of $375 and I said, thank you and NO, I'll stay in NE Texas.
My classmate took their offer and that was the last time I saw and heard of him and who knows what happened to the other guy.
Office. Entry level.
I had very little interview experience at that time. So, I didn??t think it was unusual. However, not two days later a private company called me and offers me a job. Best job I ever had. ?ÿ
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@paden-cash Me too. Conversations from 60 years ago no problem, but short term memory is iffy, especially for mundane tasks. When I sprinkle salt on my oatmeal I have to say to myself, "Putting salt on now" or I'll wonder if I did it. I think it is part of the maturation process - aka getting old.
@bruce-small?ÿ Amazing.?ÿ Thanks for sharin.
A few years back I wrote a triangle solutions system for my Casio graphing calculator. I also wrote a cogo system for it as well. Anyone that wants it and has a Casio graphic calculator I'll send them a calculator image if requested. The calculator I use (fx-9750 GII) is available at Walmart for a little less than $50. They may be up to III, but I think the two are compatible. Be sure to get Casio FA-124 from the Casio website. It's free.
@a-harris In 1966 I saw an notice from Florida Power & Light for an instrumentman position so I applied. Much better pay and benefits. First step was what seemed to be an general knowledge or maybe IQ test. Bunch of other men there, apparently for positions as grunts on the line crews, or something. I completed the test in minutes, feeling quite superior, and tried to open the door. Nothing. That door wasn't moving. One of the men graciously got up and slid the door open for me (I had never seen a sliding door before). I learned a humbling lesson that day.
I've never used a Casio. Is the programming language similar to TI Basic?
About twenty years ago I used a survey done by Florida Power & Light, I think, to gather some information for a survey I was putting together in the office. The power company survey was very well done and filled in quite a bit of information that I was missing. They were very prompt, and they sent me the survey in a nice mailing tube within days of my request.