
04132020, 09:10 PM #41


04132020, 09:13 PM #42
As a father of a 26 and a 22 year old girls, I was the lucky one to help them through their first ( and second, then third and .. ) steps in math and algebra.
They on the other hand were the unlucky ones who had to put up with my "old" methods of math and algebra.
To boot, not only old but a European version of it!
In any case, there is some method behind the madness of "new math" teaching, but it certainly isn't logical to those of us with the ancient experience.
Both kids aced the high school classes, then went onto college to ace that one too, one already has her masters, the second one is starting it in Sept.
Point of all this is that they both have told me that it was my method that got them through the "growing pains" of math learning, even though they eventually adopted
the new techniques. Showed me some of it, but most of that shit still don't make sense. It obviously works, but doesn't make sense.
As far as the original question, figuring out the area of a triangle is the only case where one need only 2 pcs of information: one side of a triangle ( base ) and the height of the triangle ( with respect to the base )
For all other calculations, you need no less or no more than 3 pcs of information, pick any combination of the 3.

04132020, 09:16 PM #43

04132020, 09:26 PM #44
Wrong example!!!
You see, giving 2 angles of a triangle already explicitly defines the 3rd angle, ergo giving 3 enclosed angles might as well be only 2!
In a similar manner, when you call a triangle a "perfect triangle", you're already providing 2 pieces of information: enclosed angles are 60 deg AND that a=b=c.
Still need 1 more and ONLY 1 more data.

04132020, 09:27 PM #45
Twice the length of the side opposite the 30 degree angle. If I remember correctly.
Bob


04132020, 09:31 PM #46

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04132020, 09:41 PM #47
Actually Janc, you could have gotten me!
Let's say you give me the information:
One angle is 30 deg, the other is 60, and one of the "lengths" is 2.
Unless you tell me what the "length" belongs to, I am still SOL.
And no, it does not need to be the length, you could have given me the area instead.
Or for that matter you could have given me the area of the inscribed circle.
Or the volume of the sphere created by the radius of the inscribed circle ....

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04132020, 09:46 PM #48

04142020, 02:31 AM #49
Perhaps this will help. And yes, the exact angles of the triangle or parallelogram do not make any difference at all. I have outlined the proof in these two drawings and at no point does any angle come into the argument except that the height is perpendicular to the base (90 degrees).
First the area of a parallelogram:
And then the area of the obtuse triangle using the parallelogram:
And the answer IS 36.
I trust that all here can mentally rotate the image in the OP's post 90 degrees to show the base at the bottom.



04142020, 02:57 AM #50
It's as simple as given in post #10. The area (AREA) of any triangle is half the base x the height.
From the info in the OP area is all that can be determined.
What does surprise me is how many suggestions have been given
To brush up on old knowledge how many 1" steel balls will weigh the same as one 2" steel ball? I'm always surprised how few get that right.

04142020, 03:11 AM #51
whoa, we're having problems with 2D here and you're adding a 3rd one... slow down there!

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04142020, 03:19 AM #52
Best one I knowt of was due to a misprint. MostlyRC homestudy school my kid brother jest retired from sent out a test with a question as meant to ask:
"Which is heavier, lead or gold?"
Time it had been socalled spellchecked, printed, and hit the field, the question was:
"Which is heavier, lead or God".
Grading for the kids was  shall we say  "finessed?"
Grading Staff wasn't in a rush to find out if THEY got it right or not, EITHER!

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04142020, 04:00 AM #53
It's been a while...but by my calculation (pen and paper, ha!) eight. Somehow, after all these years, I still have most of the mathematical formulas I've ever learned rattling around up in the old brain.
The "new math" is something they came up with to try to make it easier for everyone to learn faster and push through more material quicker from what I gather. But it seems like it makes some things easier and some more of a pain in the butt to grasp.
I teach my kids the way that works for them and the way they think through things individually. If they bring something home and don't understand it, then we go over it a few different ways until they do. If that isn't the teacher's preferred way, tough shit for the teacher. I am willing to go to the school about that if I need to. Haven't had to so far. Correct is correct if it's been arrived at with proper methodology.
My kiddos both learned to read before kindergarten using the same book I learned with. They both knew their basic multiplication and division before the teacher ever brought it up in class. Giving them a good head start helps a lot. Also teaching them to look at things from different "angles" or perspectives when they don't understand something forms good habits for future learning of any subject.

04142020, 04:07 AM #54
Is it ? the "new math" I am aware of started with SMSG and was based on teaching set theory. It was more mathematics, less arithmetic. Parents didn't like it then, either, cuz they couldn't do the homework
But that was over 60 years ago ...
by gosh, it's on wikipeedia...
https://web.math.rochester.edu/peopl...rarm/smsg.html
Worth a read. Funny.

04142020, 04:09 AM #55

04142020, 04:14 AM #56

04142020, 04:17 AM #57

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04142020, 05:19 AM #58
the ammount of surface space contained within its borders.

04142020, 05:30 AM #59
Set theory is the right place to start for training a mathematician, not a human calculator which is what math education is geared towards. Set theory is the very most basic & therefore abstract underpinning of mathematics.
Cutting a piece of paper and rearranging the pieces is not a proof but rather a demonstration of a particular case.

04142020, 05:31 AM #60
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