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#1 2013-08-10 04:23:49

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Help needed with a simple question.

Hi everyone. As i said in my intro I am a welder. I've been asked to construct a spiral made up of triangles.  Like most jobs I have sat down to draw it out and make cutting lists etc so I can give the customer a fair estimate of cost.
   After doing the old A2+B2=C2 a few times to work out the lengths of the sides I notices I no longer need to do that. The answer for the next triangle is always in the previous one.
  E.G If the next A or B is the previous c, then the next c is the previous a+b.(to my level of accuracy anyway lol)
This got me thinking,how would I describe this change of value in math 'talk'.
I'm more interested in the way it would be described than the lvl of accuracy.


I know this is probably a simple question and apologies if I offend anyone.
Thank you all in advance for your patience.

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#2 2013-08-10 04:27:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Help needed with a simple question.

E.G If the next A or B is the previous c, then the next c is the previous a+b.

Is a and A the same? Is b and B the same?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-08-10 04:30:16

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

yes, sorry, my mistake.

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#4 2013-08-10 04:39:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Help needed with a simple question.

If A + B = C

what about D, is it B + C?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2013-08-10 04:41:57

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

To clarify, I know the statement
" If the next A or B is the previous C, then the next C is the previous A+B"
is probably not very accurate. I guess I'm trying to find out how this would be wrote as a formula that describes how the value of A,B and C change. I know its probably childishly simple to most of you. I would be eternally grateful if someone would point me in the right direction and I'll try and learn more.

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#6 2013-08-10 04:50:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Help needed with a simple question.

Hi;

Try to describe the process without resorting to any math. There is a rule that if you can not state it in words you do not understand the problem well enough to solve regardless of how much math you know.

Think about the process itself and then describe it as if you were talking to your Grandmother. Take your time.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2013-08-10 04:51:52

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

bobbym wrote:

If A + B = C

what about D, is it B + C?

A quick look around suggests I need to be looking into recursive,would that be right? thanks for your help, much appreciated tongue

Last edited by bill.stead (2013-08-10 04:52:41)

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#8 2013-08-10 05:01:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Help needed with a simple question.

That is where I was trying to take you.

But I still think before you look at any math you should be able to state the problem, in your own language. It may be a simple recursion a[n]=a[n-1]+a[n-2] or it may be something else.

If you can not clearly state the problem then post the measurements.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2013-08-10 05:27:25

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

ok, if we start with an equal triangle number 1 with short sides 2m. Then the long side is 2.8m. That then becomes one of triangle number 2's short sides.so triangle number 2s long side is 4m. that then becomes a side for triangle number 3, etc etc.that creates a spiral made of triangles that increase in size in relation to the previous triangle. (I've rounded the math up a bit).
using what you put above, the closest I can get right now is (using a,b,and c )
   c[n]=c[n-a+b]
but that only looks to be part of it.

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#10 2013-08-10 05:34:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Help needed with a simple question.

Hi;

2's short sides.so triangle number 2s long side is 4m.

How does that happen?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2013-08-10 05:34:14

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Help needed with a simple question.

So you have

T1                2, 2, 2√ 2

T2                2√ 2,  2√ 2,  4

T3                4, 4, 4√ 4

etc

??

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2013-08-10 05:52:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Help needed with a simple question.

That is what I mean T3 is impossible.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2013-08-10 06:32:30

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Help needed with a simple question.

These triangles are spiralling upwards.  Does that help?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2013-08-10 07:11:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Help needed with a simple question.

How can the sides violate the triangle inequality?

When he mentions the sides I assume he means the sides of the triangle.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#15 2013-08-10 07:18:05

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Help needed with a simple question.

Sorry.  My mistake.  When I'm 'on the case', my maths jumps ahead so fast, my arithmetic cannot keep up.  You will have seen me do this sort of thing many times.  What I meant was

T3                4, 4, 4√2

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#16 2013-08-10 07:57:55

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

Would it help if I put up a quick drawing to explain what prompted the question?
I have to admit I'm not sure the real world application would stand up to a detailed formula.
The idea was to be able to work out the total design with nothing more than one measurement and a formula.However I was more interested in how such a formula would be expressed rather than if it would work. I could only get it to work by rounding everything to 2 decimal places.I'm not even sure if it would work at  larger scale.

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#17 2013-08-10 08:08:24

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Help needed with a simple question.

Drawing would be good.

B


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#18 2013-08-10 08:46:59

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

This is the drawing for half of a window frame to be welded up.

View Image: window2.jpg

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#19 2013-08-10 08:53:33

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

As you can see from the above drawing, each triangle is extrapolated from the one below.
All measurements in cm.
if you were given the first measurement, eg 15 cm, how would you express a formula to calculate the rest.
Yes I know if I did not round it all to 2 decimal place it would not work. The point is I don't need .o1 of a cm accuracy to build this in the real world. Can this sort of 'error' be built into a math formula?

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#20 2013-08-10 08:56:40

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Help needed with a simple question.

OK thanks.

So here's the recursive formula:

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#21 2013-08-10 09:01:27

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Help needed with a simple question.

so

I would work accurately for all steps and round off as appropriate.  Otherwise the rounding errors will accumulate.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#22 2013-08-10 09:30:05

bill.stead
Member
Registered: 2013-08-10
Posts: 10

Re: Help needed with a simple question.

Thank you both very much for your patience . I can see I have a long road ahead of me to understand all of that. At least I know what to look for now.

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