angles help

denis_gylaev · 2016-05-05 11:02:19

https://gyazo.com/0a81ab3e6b02fe087d599a5a08bef1c9

is 19.5 right?

Last edited by denis_gylaev (2016-05-05 11:05:34)

bobbym · 2016-05-05 13:46:41

Hi;

That is what I am getting.

phrontister · 2016-05-07 00:42:51

I also got 19.5°

bobbym · 2016-05-07 00:46:23

Gebra! Gebra! It is the man. If it can not do it nobody can, yay Geeeebra!

phrontister · 2016-05-07 00:49:46

Did it without G, but got it to check my work. I hadn't realised until then that there can be a variety of shapes.

bobbym · 2016-05-07 00:55:00

Did it without G

So, you did it the hard way.

phrontister · 2016-05-07 01:01:43

Yes...wanted to see if I could still rough it, with no mod cons.

bobbym · 2016-05-07 01:05:13

Sometimes, that is the best way.

thickhead · 2016-05-07 01:19:28

I am unable to understand the discussion. it was about calculation of an angle but I am unable to follow the thread.

phrontister · 2016-05-07 01:25:39

Sorry...can't reply right now, coz Nadal just broke Murray who was serving for the match, and they're back on serve again.

Edit: It's over...Murray broke right back again, for his second win ever against Nadal on clay.

Last edited by phrontister (2016-05-07 01:27:45)

phrontister · 2016-05-07 02:15:20

thickhead wrote:

I am unable to understand the discussion. it was about calculation of an angle but I am unable to follow the thread.

Post #4 is just a chant that's popularly used in support of a favourite something or other, which is usually a person but in this case is the freeware geometry program Geogebra, for which some of us here on MIF 'affectionately' use the "Gebra" abbreviation (I tend to use "G"). "M" for "Mathematica" is another example.

bobbym and I like to use G to help solve geometry problems, but on this occasion I felt the need (urge?) to go the manual route: pen and paper.

So, once we had both solved the problem and confirmed the OP's answer, our discussion turned to the weightier matter ( ) of which solution method to use: software or 'hard'ware [sic]:

bobbym wrote:

So, you did it the hard way.

bobbym · 2016-05-07 02:43:13

I am unable to understand the discussion.

Just some strange vernacular. I am advocating the experimental way of doing mathematics.

Bob · 2016-05-07 18:37:12

I used Euclidean geometry and algebra:

Let AXB = ABX = x : XBC = y : and ACB = z

x = y + z (external angle of a triangle XBC is sum of two internal opposites) ..... (1)

x + y - z = 39 (given)

Substitute (1) into the above

y + z + y - z = 39 => 2y = 39 => y = 19.5

Bob

ps. Would you like to see an example to show why experimental maths is not always reliable ?

Agnishom · 2016-05-07 19:30:26

Yeah.

Are you going to site the conjecture that Euler made which was disproved when faster computation was available?

Bob · 2016-05-07 21:30:08

hi Agnishom,

I've not heard of that. No, my example isn't even about geometry.

Back when I taught classes, I had a sequence of lessons on 'The Nature of Proof'. It only touched the surface, of course, but I was trying to show why mathematicians want to prove things and give some ideas about how they go about it.

My introduction was this:

Consider the quadratic

Pick a counting number for n and evaluate the formula. Is the result a prime number?

n=1, formula = 43 This is a prime.
n=2, formula = 47 This is a prime.
n=3, formula = 53 This is a prime.
........
n= 20, formula = 461 This is a prime.

You might like to try a few values for n yourself.

By the time I'd been round the class and everyone had had a go, they were happy to agree that this formula generates primes.

If you've spotted a value of n that disproves this, well done!

If you set it up on a spreadsheet, you can try out a lot of values. You will find it is 'prime heavy', at least for quite a while; I haven't tried all values of n.

And that's the point. Just because a result keeps on happening, doesn't mean it will keep on happening.

What is the first value of n which doesn't give a prime? And the next ? Say this one is 'm'. You'll find that m+1 gives another prime, and then there's another long sequence of primes before the next non prime.

Conclusion. Just because an 'experiment' generates lots of confirming results doesn't prove that result is true.

I've probably told this before (sorry) but in another lesson a pupil taught me something. For years I had done the following:

Get everyone to draw a triangle (any will do); measure the angles and add them up. If you have a class of 30, you'll get lots of answers such as 178, 179, 180, 181, 182. Up until this particular day the classes had always been happy to conclude that the angles of a triangle add up to 180 and the variation is just experimental error chiefly because of the thickness of the datum lines on the protractor. But this one time a pupil came up with a different answer. He said the angles of a triangle always add up to a number that is close to 180. On the basis of the data you cannot fault him. Worth a gold star I think.

Anyway, do tell me about the Euclid conjecture. Thanks,

Bob

Agnishom · 2016-05-07 22:12:59

That brings us to an interesting question: Given an arbitrarily large n, is there always a quadratic p, such that p(1), p(2), ..., p(n) are all prime?

https://en.wikipedia.org/wiki/Euler's_s … conjecture

By the way, how have you been? Long time since we talked

Last edited by Agnishom (2016-05-08 04:26:33)

phrontister · 2016-05-07 23:23:09

Hi Bob;

I didn't know that the "external angle of a triangle XBC is sum of two internal opposites", and I came to x = y + z differently:

BXC = 180 - x
∴ y = 180 - z - (180 - x) => y = x - z (or, x = y + z)

The rest was the same.

Ah...the 'exterior angle theorem' is right here.

Last edited by phrontister (2016-05-08 13:35:46)

bobbym · 2016-05-07 23:49:32

Hi Bob;

A short, hopefully readable preparation for the below.

http://www.mathisfunforum.com/viewtopic.php?id=19346

Would you like to see an example to show why experimental maths is not always reliable ?

Something does not have to work all the time to be useful. It just has to work a high percentage of the time and EM used effectively has a very high percentage.

Drawing the conclusion that they are all primes from just 20 examples is not good EM. I do not become interested in a conjecture until I see a couple of million examples at least. That prime example demonstrates the power of EM because anyone using EM would find the 41 st counterexample extremely quickly. He does not need to notice that 41^2 + 41 + 41 is obviously divisible by 41. In my view, EM adheres to the "Teakettle Principle" much more than traditional math does.

He said the angles of a triangle always add up to a number that is close to 180. On the basis of the data you cannot fault him.

If he said that to me I would immediately ask how close. A number is not worth much unless we can bound it. If he can correctly say

179.56 < the sum of the angles < 180.3 and then

179.9 < the sum of the angles < 180.1

179.995 < the sum of the angles < 180.003

179.999995 < the sum of the angles < 180.000021

179.999999999999999999712 < the sum of the angles < 180.000000000000000113

I am becoming interested. The bounding suggests a novel idea, If he now showed that the sum of the angles of a triangle is always an integer and since 180 is the only integer between those bounds I would stare in amazement. Finally, a student that does not just quote what Euclid/Euler did back at me.

When I do experimental work I require four things:

1) Lots and lots lots of evidence (millions or billions) and a conjectured answer derived in at least two different ways.

2) A bound on the conjectured answer.

3) The probability ( guesstimate is often enough ) that this conjectured answer is right.

If I know the conjectured answer is going to be wrong less than 1 time in 10 million I certainly am going to use it on forums or for schoolwork especially if I have the other requirements as well. Of course human error sneaks in from time to time. I was reading an article which claimed that out of the 750 thousand traditional proofs submitted to their journal close to half contained errors!

Agnishom · 2016-05-08 04:25:43

Notice that he does not have a fast computer. He is still doing very good experimental work.

---

Mandatory xkcd reference: Lookup "experimental monotheism"

bobbym · 2016-05-08 08:17:29

In the immortal words of grandpappyd, "he who, he who." I still do not know what he meant.

Agnishom · 2016-05-08 15:14:44

I still do not know what "He who, he who" means.

Experimental Monotheism is a religion where you claim there is one god to begin with, but try to count the error bars on that number

bobbym · 2016-05-08 15:36:38

Error bars?

Agnishom · 2016-05-09 22:01:35

A number by itself is useful, but it is far more useful to know how accurate or certain that number is.
-bobbym

bobbym · 2016-05-10 04:53:21

I remember that quote but error bars?

Agnishom · 2016-05-10 22:07:34

I do not know what they are exactly called. I have not done so much numerical work

Math Is Fun Forum

#1 2016-05-05 11:02:19

angles help

#2 2016-05-05 13:46:41

Re: angles help

#3 2016-05-07 00:42:51

Re: angles help

#4 2016-05-07 00:46:23

Re: angles help

#5 2016-05-07 00:49:46

Re: angles help

#6 2016-05-07 00:55:00

Re: angles help

#7 2016-05-07 01:01:43

Re: angles help

#8 2016-05-07 01:05:13

Re: angles help

#9 2016-05-07 01:19:28

Re: angles help

#10 2016-05-07 01:25:39

Re: angles help

#11 2016-05-07 02:15:20

Re: angles help

#12 2016-05-07 02:43:13

Re: angles help

#13 2016-05-07 18:37:12

Re: angles help

#14 2016-05-07 19:30:26

Re: angles help

#15 2016-05-07 21:30:08

Re: angles help

#16 2016-05-07 22:12:59

Re: angles help

#17 2016-05-07 23:23:09

Re: angles help

#18 2016-05-07 23:49:32

Re: angles help

#19 2016-05-08 04:25:43

Re: angles help

#20 2016-05-08 08:17:29

Re: angles help

#21 2016-05-08 15:14:44

Re: angles help

#22 2016-05-08 15:36:38

Re: angles help

#23 2016-05-09 22:01:35

Re: angles help

#24 2016-05-10 04:53:21

Re: angles help

#25 2016-05-10 22:07:34

Re: angles help

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