If it had been taught like that I might have done better in in school. I was good with Geometry because 1, I had a good teacher, and 2, I could see the mechanical aspect of the problems.
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Originally posted by Rich Carlstedt View PostDave, You are right, Trig is awesome !
I came up with the triangle method for my good friend whom I have taught machining, but he has dyslexia and math is very difficult for him
I do Trig in my head and taught math to machinists when I worked in a shop..
Trrig is not hard, but our education system is screwed up and they scare the hell out of math students with overboard complications.
FIRST , Trig is nothing more than a fraction The same as 1/3 or 1/4 are fractions so understand you have a fraction or as I prefer to say " A Ratio"
Some of these ratios' are simple, and if you know that. it can make your calculations a piece of cake.
For example, what was the first commercial jetliner in the USA ?
It was the Boeing 707 ......hooray ..got it... now what is 2 times 707 ? ..its 1414 Easy ? Yes
Now you will never have a problem with squares and a diagonal line to opposite corners
It's right triangle OK ...So if the straight legs are "1" then the diagonal is 1.414
If the diagonal is "1" , then the legs are .707 ...see the relationship ?
No Trig, but if you have a square that is 3 inches square, you know the diagonal is ( 3 x 1.414) 4.242 "
So the Math becomes simple multiplication
If you were teaching trig, you'd show them how to derive the length of the diagonal (Pythagoras), and then go on to show why sin(45) = cos(45) = 1/sqrt(2) = sqrt(2) / 2 = 0.707 Then you could generalize the approach to any right triangle and they would have learned something they could use as a framework on which to build further trig understanding. Maybe that sounds like "overboard complications" to you; to me it sounds like a good teaching plan.
It's true that math teachers seldom spend time explaining why students need to learn the subject to do well in the real world. However, I think there is another reason why students have so much trouble with math. In almost all their other courses there is considerable latitude for what is "correct" or "good". Literature, art, music, history, language all offer opportunity for personal interpretation and development of tastes. Math is the exact opposite: there is only one "right" answer and wrong answers are easily so demonstrated. The only freedom is the analysis avenue one uses to get to the answer and even there there are strict rules that must be followed. Young people are not tolerant of such discipline and their response is to avoid it.
Regards, Marv
Home Shop Freeware  Tools for People Who Build Things
http://www.myvirtualnetwork.com/mklotz
Location: LA, CA, USA
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Originally posted by mklotz View PostSounds to me like you're teaching memory devices (Boeing 707) and arithmetic (2 times 707) rather than teaching trig.
If you were teaching trig, you'd show them how to derive the length of the diagonal (Pythagoras), and then go on to show why sin(45) = cos(45) = 1/sqrt(2) = sqrt(2) / 2 = 0.707 Then you could generalize the approach to any right triangle and they would have learned something they could use as a framework on which to build further trig understanding. Maybe that sounds like "overboard complications" to you; to me it sounds like a good teaching plan.
It's true that math teachers seldom spend time explaining why students need to learn the subject to do well in the real world. However, I think there is another reason why students have so much trouble with math. In almost all their other courses there is considerable latitude for what is "correct" or "good". Literature, art, music, history, language all offer opportunity for personal interpretation and development of tastes. Math is the exact opposite: there is only one "right" answer and wrong answers are easily so demonstrated. The only freedom is the analysis avenue one uses to get to the answer and even there there are strict rules that must be followed. Young people are not tolerant of such discipline and their response is to avoid it.
The reason for the simile of the airliner is to make the numbers more acceptable to nonmath machinists and to teach them to think in ratios
Machinists in general can do math, but it's the "TRIG"wall they stop at. Now a great advance has been made with calculators in the past 40 years
and that helps .. however I see the same "Blank Stare in the bright headlights" with young machinists if they don't have a CAM program to do the work..
Here is another shortcut for the brain ....and math impaired
Know the number 17 .... & Know that both Sine and Tangent are almost the same for the first 10 degrees of angle..
so that means .017 per INCH per DEGREE
So, if you have a Sine plate with 5 inch setting centers, and you want a 3 degree angle  you need 5 x 17 (=85) x 3= 255
so the "approximate spacer (Jo Block) of .255" is needed to get a 3 degree angle... now here is the important point, the machinist can do his
calculations on his calculator and know he is right if his answer is .2616 as he is really close to the top of the head figure ( .255) and the error is only 2 1/4 percent
Anyway Marv thanks for all you do for helping the hobby, your website is a treasure trove.
Rich
Green Bay, WI
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I've always used the rule of thumb 0.0175" (17 and a half thousandths) /degree/inch for very small angles.12" x 35" Logan 2557V lathe
Index "Super 55" mill
18" Vectrax vertical bandsaw
7" x 10" Vectrax mitering bandsaw
24" State disc sander
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