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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




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Topic review (newest first)

2013-08-11 07:30:05

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.

bob bundy
2013-08-11 07:01:27


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


bob bundy
2013-08-11 06:56:40

OK thanks.

So here's the recursive formula:


2013-08-11 06:53:33

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?

2013-08-11 06:46:59

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

bob bundy
2013-08-11 06:08:24

Drawing would be good.


2013-08-11 05:57:55

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.

bob bundy
2013-08-11 05:18:05

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


2013-08-11 05:11:42

How can the sides violate the triangle inequality?

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

bob bundy
2013-08-11 04:32:30

These triangles are spiralling upwards.  Does that help?


2013-08-11 03:52:03

That is what I mean T3 is impossible.

bob bundy
2013-08-11 03:34:14

So you have

T1                2, 2, 2√ 2

T2                2√ 2,  2√ 2,  4

T3                4, 4, 4√ 4




2013-08-11 03:34:10


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

How does that happen?

2013-08-11 03:27:25

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 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 )
but that only looks to be part of it.

2013-08-11 03:01:11

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.

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