Trigonometry formula and answer

[Barrykgerdes]

This is a bit off topic but may be of some interest to the guru's and nerds.

I refered to doing an aerial measurement using manual mathmatical calculations. The actual project was quite involved at the time. I was working with two engineers who had a project to find out why some of our HF aerials gave peculiar results when attached to automatic aerial tuners.

The engineers did some research through IEEE papers and manuals and discovered that very little had been published in this area since the early 1920's. We set about to confirm previous work and hopefully come up with some new data. The total project took about 3 months and the aerial work I did took about a month. (1969)

At this time all the measurements had to be done manually followed by lots of math calculations. About 12 months later HP showed us a machine that could be hooked to the aerial and produce a Smith Chart in seconds. A job that took me near a month. Ah such is progress!

Barry

[sjastro]

Originally Posted by Robh

Oversight in expansion ...
a^2 = (2n+1)^2 = 4n^2+4n+1 = (2n^2+2n) + (2n^2+2n+1)

Therefore can select
b = 2n^2+2n = n((2n+1)+1) = n(a+1)
c = 2n^2+2n+1 = b+1

However, the end result still works out the same.
For any odd integer a, you can always find two consecutive integers b,c to complete the triad.
e.g. a = 9
a = 2n+1 = 9 ---> n = 4
b = n(a+1) = 4(9+1) = 40
c = 40+1 = 41
Triad 9,40,41.

Interesting.
Thanks for that, Rob.

Now the question is if there is a case where "a" is an even integer for the Liethagoras condition to be true?

Regards

Steven

[Robh (Rob)]

Originally Posted by sjastro

Now the question is if there is a case where "a" is an even integer for the Liethagoras condition to be true?

Regards

Steven

Not possible.
If a = 2n then a^2 = 4n^2, which is also even.
However, c-b = 1 implies one of b or c is even, the other odd.
Therefore b+c is odd.
i.e. a^2 cannot equal b+c as LHS is even but RHS is odd.

Regards, Rob.

[sjastro]

Originally Posted by Robh

Not possible.
If a = 2n then a^2 = 4n^2, which is also even.
However, c-b = 1 implies one of b or c is even, the other odd.
Therefore b+c is odd.
i.e. a^2 cannot equal b+c as LHS is even but RHS is odd.

Regards, Rob.

Of course. I should have seen that.

Thanks

Steven

[TrevorW]

Draw a base line to scale

use a protractor to mark your angles then draw lines till they intersect

then

measure with a ruler will give the length of each side

simple

[Paul Haese]

Have not seen sine for such a long time. Imagine however trying to find the length of a side which is curved and then you have spherical trigonometry. You use this for working out horizontal and vertical control for map making.

Thanks for the refresher lesson.

[Barrykgerdes]

Originally Posted by TrevorW

Draw a base line to scale

use a protractor to mark your angles then draw lines till they intersect

then

measure with a ruler will give the length of each side

simple

That reminds me of our learning Pythagoras theorem:
We proved it in Mathmatics first
Then we proved it "practically" in science by constructing a rt angle triangle on graph paper and counting squares.

The only "calculators" we had in those days were the standard issued maths tables sine,cos,tan and log, fingers or a sliderule.

Barry