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March 2nd, 2017, 06:31 PM   #11
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Hi skipjack,

That's a very good lead and useful information. Let me play around with that a little and I'll let you know the results of what I find!!!
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March 3rd, 2017, 02:33 AM   #12
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That's a good spot SkipJack!

So basically the function seems to behave something like

$\displaystyle f(x) = x/45 - tan x$

but if the tan x evaluates to infinity, it just sets it to zero.

Can you try working out the function with angles of 60, 65 and 70 (starting from a 'value' of zero) and see if you get -0.23208, -0.5195 and -1.1919?
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March 9th, 2017, 12:36 PM   #13
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Quote:
Originally Posted by skipjack View Post
Note that 4.57735... = 4 + 1/√3 and 7.42265... = 8 - 1/√3, and that tan(30°) = 1/√3.
Hi skipjack,

Your 'note' has proven very helpful of pointing me in the right direction to solving my problem. Thank you very much skipjack!
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March 10th, 2017, 09:24 PM   #14
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I'm needing to find a formula that will allow me to calculate values around the circumference of a static size circle. The table below describes the circle size and the values around the circumference every 22.5 degrees apart.

With the help from skipjack I was able to create these formulas that match my software values:

Start...Degrees.....Result...........Formula...... .........Formula
0.............0.............0...................0. ........................0
0..........22.5......0.414214...... sqrt(2) - 1.............tan(22.5)
0............45..........1...................sqrt( 1)................tan(45)
0..........67.5......1.585786.......3 - sqrt(2)........2 - tan(22.5)
0........... 90..........2..............sqrt(1) + 1..........tan(45) + 1
0........112.5......2.414214......1 + sqrt(2).......tan(22.5) + 2
0..........135..........3..............sqrt(1) + 2..........tan(45) + 2
0........157.5......3.585786.......5 - sqrt(2)........4 - tan(22.5)
0..........180..........4..............sqrt(1) + 3..........tan(45) + 3
0........202.5......4.414214.......3 + sqrt(2)..... tan(22.5) + 4
0..........225..........5..............sqrt(1) + 4......... tan(45) + 4
0........247.5......5.585786.......7 - sqrt(2)........6 - tan(22.5)
0..........270..........6..............sqrt(1) + 5..........tan(45) + 5
0....... 292.5......6.414214.......5 + sqrt(2)......tan(22.5) + 6
0..........315..........7..............sqrt(1) + 6......... tan(45) + 6
0........337.5......7.585786.......9 - sqrt(2)........8 - tan(22.5)
0..........360..........8..............sqrt(1) + 7..........tan(45) + 7

What I can't figure out is how to calculate other 22.5 degree values by starting at a point other than zero. Here are some random starting points with the answer from a software program but I need a formula to show me how that answer was obtained:

Starting at 2.1 and travel 22.5 degrees returns a value of 2.536433
Starting at 2.1 and travel 67.5 degrees returns a value of 3.698284

Starting at 3.5 and travel 22.5 degrees returns a value of 3.928932
Starting at 3.5 and travel 67.5 degrees returns a value of 4.867295

Again, thanks for any help.
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March 12th, 2017, 01:15 PM   #15
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Can you give some additional values based on starting at values less obscure than 2.1 and 3.5?
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March 12th, 2017, 01:24 PM   #16
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Quote:
Originally Posted by skipjack View Post
Can you give some additional values based on starting at values less obscure than 2.1 and 3.5?
I should be able to provide any starting point with the answer using the software with any number between 2 - 10. Please give me a list of numbers you want.

Last edited by Frankenstein2; March 12th, 2017 at 01:26 PM.
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March 12th, 2017, 01:55 PM   #17
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Could this program have anything to do with Mohr Circles, which are often offset from the origin?

https://www.google.co.uk/search?hl=e...85.FfsaG8peeUY
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March 12th, 2017, 02:16 PM   #18
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Quote:
Originally Posted by Frankenstein2 View Post
Please give me a list of numbers you want.
Try a starting value of 7.5.
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Last edited by skipjack; March 12th, 2017 at 03:59 PM.
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March 12th, 2017, 02:37 PM   #19
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Quote:
Originally Posted by skipjack View Post
Quote:
Originally Posted by Frankenstein2 View Post
Please give me a list of numbers you want.
Try a starting value of 7.5.
Starting at 7.5 and travel 22.5 degrees FORWARD returns a value of 7.928932
Starting at 7.5 and travel 22.5 degrees BACKWARD returns a value of 6.867295

Starting at 7.5 and travel 45 degrees FORWARD returns a value of 8.333333
Starting at 7.5 and travel 45 degrees BACKWARD returns a value of 6.333333

Starting at 7.5 and travel 67.5 degrees FORWARD returns a value of 8.867295
Starting at 7.5 and travel 67.5 degrees BACKWARD returns a value of 5.928932

Starting at 7.5 and travel 90 degrees FORWARD returns a value of 9.5
Starting at 7.5 and travel 90 degrees BACKWARD returns a value of 5.5

Last edited by skipjack; March 12th, 2017 at 03:59 PM.
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