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Main Forums => The Roundtable => Topic started by: castle key on August 13, 2019, 05:26:39 PM

Title: Math actually works!
Post by: castle key on August 13, 2019, 05:26:39 PM
I am laying out a construction project, a bocce court. The basic gist is a 10 foot by 60 foot outline with poles every ten feet. These poles will have overhead stuff to create a pergola.

I pondered laying out an accurate right angle at the corners and had that "aha moment" that I could set marks for the 60' line, mark off ten foot increments for each of the poles, and as the width was equal to the run to the first mark, the hypotenuse was my answer!

Of course, I couldn't remember the formula, but a quick search gave the answer.

And I thought I would never use geometry again after middle school.

Mrs. Castle Key and I decided that few of today's children would have any clue how to do this simple calculation or even where to begin trying. I weep for our future.
Title: Re: Math actually works!
Post by: WLJ on August 13, 2019, 05:51:00 PM
But AOC says math = free
Title: Re: Math actually works!
Post by: K Frame on August 13, 2019, 06:40:18 PM
3, 4, 5

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Title: Re: Math actually works!
Post by: 230RN on August 13, 2019, 10:03:15 PM
Obligatory:

https://en.wikipedia.org/wiki/The_Feeling_of_Power

I've noticed that with a person of considerable mechanical skills.  In determining tailstock setover for a cut of a given angle, he'd rather resort to the internet or CAD system than use the actual math concepts.

Fun, classic:

    (http://thumbpress.com/wp-content/uploads/2013/07/funny-tangerine-math-pun1.jpg)

^ Also obligatory.

Heaven help us if the internet ever collapses totally.

Terry, 230RN

Slooshun:

In the trigonometric identity:

 sin(θ) ÷ cos(θ) = tan(θ)

Subsituting the variable "gerine" for theta, we get:

sin(gerine) ÷  cos(gerine)  = tan(gerine)

Image credit in properties.
Title: Re: Math actually works!
Post by: French G. on August 13, 2019, 10:45:16 PM
I would set the four corners first, make sure you have your ten and sixty as close as you can, then just measure corner to corner. If the measurement is the same then you have a good rectangle, no matter what that measurement is. I cough up a hypotenuse every now and then welding when I have no other way to check square, but use corner to corner daily. Once the corners are good do everything else on a string line.
Title: Re: Math actually works!
Post by: Hawkmoon on August 14, 2019, 12:34:24 AM
I am laying out a construction project, a bocce court. The basic gist is a 10 foot by 60 foot outline with poles every ten feet. These poles will have overhead stuff to create a pergola.

I pondered laying out an accurate right angle at the corners and had that "aha moment" that I could set marks for the 60' line, mark off ten foot increments for each of the poles, and as the width was equal to the run to the first mark, the hypotenuse was my answer!


I don't understand what you did, but I'm not going to admit it.
Title: Re: Math actually works!
Post by: castle key on August 14, 2019, 06:28:46 AM
I would set the four corners first, make sure you have your ten and sixty as close as you can, then just measure corner to corner. If the measurement is the same then you have a good rectangle, no matter what that measurement is. I cough up a hypotenuse every now and then welding when I have no other way to check square, but use corner to corner daily. Once the corners are good do everything else on a string line.

I sort of did that, but I don't think you can really set all four corners by eye and get them square.

I set one long run, a sixty footer, and pulled a line. That side would be straight. I then did the ten foot measurements, which is manageable and a good start to get the square. Am I missing something from your thoughts to set four corners and then nudge it around a bit?

The real fun will be setting the 6 x 6 uprights and getting them accurately in line. Those are big "logs" over a long run. Thoughts?
Title: Re: Math actually works!
Post by: dogmush on August 14, 2019, 09:05:29 AM
When I used to set a long line of fence posts we'd just use a level and a string.  Bring the outside face to the string line and make sure it's vertical.

Title: Re: Math actually works!
Post by: French G. on August 14, 2019, 10:03:23 AM
If four points measure the same across the diagonals the only possibilities are you built a rectangle or a trapezoid. And if your sixty and ten are correct, then you are there. I think you came out fine, similar method in steps. Now the real question, how the hell do you play bocce?
Title: Re: Math actually works!
Post by: HeroHog on August 14, 2019, 10:18:10 AM
All I remember is a^2+b^2=c^2
Title: Re: Math actually works!
Post by: 230RN on August 14, 2019, 10:46:25 AM
a is not square, a is cool.

(Dredged up from the few remaining memories of high school.)
Title: Re: Math actually works!
Post by: HeroHog on August 14, 2019, 10:50:41 AM
Pie arn't square, boy, pie are round, cornbread (sweet) are square!
Title: Re: Math actually works!
Post by: Hawkmoon on August 14, 2019, 11:09:11 AM

I set one long run, a sixty footer, and pulled a line. That side would be straight. I then did the ten foot measurements, which is manageable and a good start to get the square. Am I missing something from your thoughts to set four corners and then nudge it around a bit?


What you missed is where French G. mentioned putting in all four corner posts and comparing the diagonal measurements. Putting in two corners and the intermediate ten-foot points only gives you a line, not a rectangle. The intermediate ten-foot points don't do anything to help make the corners 90-degrees.
Title: Re: Math actually works!
Post by: bedlamite on August 14, 2019, 11:14:14 AM
Pie arn't square, boy, pie are round, cornbread (sweet) are square!

That's just your opinion. But without pi, it's just an onion.
Title: Re: Math actually works!
Post by: AZRedhawk44 on August 14, 2019, 11:20:03 AM
3, 4, 5

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Nope.  that's for a 30-60-90 triangle, if I remember correctly.

He's looking for an equilateral right triangle.  90-45-45.

That is 1, 1, sqrt(2).

Given a 60x10 rectangle and support posts every 10 feet along the 60 foot side, you would have a series of 10x10 squares all in a row:

|=|=|=|=|=|=|

The hypotenuse of one section (|=|) is of a 10x10 square.

|\|

a^2 + b^2 = c^2.

100 + 100 = c^2

c = sqrt(200) = 14.14 feet.

All that assumes I understood the correct hypotenuse you were looking for.


ETA:  A 3/4/5 triangle evidently doesn't have 30/60/90 degree angles.  They're odd numbers.
Title: Re: Math actually works!
Post by: bedlamite on August 14, 2019, 11:29:19 AM
3,4,5 triangle has angles of about 53.1, 37.9, and 90.

Why do I even remember that? Nevermind, I don't want to know.
Title: Re: Math actually works!
Post by: castle key on August 14, 2019, 12:27:37 PM
Once I get the verticals set and and installed, I will need to place horizontal cross pieces at the tops. These need to all come out level. Further, I need to grade the ground and put in the surface, which will be about 8-10 inches deep, and must be level.

I was thinking of using a laser level to mark all of my points. What think you all?

If a laser is the suggestion, please suggest brands/tools, understanding that I don't really want to spend a gazillion dollars. Point lasers, rotary lasers, green/red? The measurement run will be about 60 feet.
Title: Re: Math actually works!
Post by: AZRedhawk44 on August 14, 2019, 01:01:31 PM
I'd say just use a good long beam level on each support.

Put your vertical footers in concrete blocks like this:

https://www.homedepot.com/p/7-3-4-in-x-10-1-2-in-x-10-1-2-in-Concrete-Pier-with-Strap-Block-100002710/100321949

Level the blocks by adding sand under the low ones.

Then haul in your substrate for your ground (is it rock?  sand?  Not familiar with bocce ball play conditions).  Fill even with the concrete blocks and they won't slide around anywhere.
Title: Re: Math actually works!
Post by: grampster on August 14, 2019, 01:01:36 PM
 sin(θ) ÷ cos(θ) = tan(θ)

sin is doing it on the beach.   The cos(t) does equal a tan if the sin is during the day.  It also leads to skin cancer. :old:
Title: Re: Math actually works!
Post by: bedlamite on August 14, 2019, 01:04:42 PM
 sin(θ) ÷ cos(θ) = tan(θ)

sin is doing it on the beach.   The cos(t) does equal a tan if the sin is during the day.  It also leads to skin cancer. :old:

Don't be so obtuse.
Title: Re: Math actually works!
Post by: K Frame on August 14, 2019, 08:18:00 PM
3, 4, 5 gives a perfect right angle.

Multiple them by the same number, any number, and you get a right angle.

Using that to set your baselines you can lay out any number of sections of equal dimension.

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Title: Re: Math actually works!
Post by: AZRedhawk44 on August 14, 2019, 10:16:44 PM
3, 4, 5 gives a perfect right angle.

Multiple them by the same number, any number, and you get a right angle.

Using that to set your baselines you can lay out any number of sections of equal dimension.

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Yes it does, but not for a 10' x 10' triangle.

His dimensions between posts is 10x10.  To ensure all corners are square, the diagonals of a 10x10 square must be sqrt(200), or about 14.14 feet.

3/4/5 doesn't matter here.  Different triangle, different relationship.
Title: Re: Math actually works!
Post by: zxcvbob on August 14, 2019, 10:28:10 PM
Yes it does, but not for a 10' x 10' triangle.

His dimensions between posts is 10x10.  To ensure all corners are square, the diagonals of a 10x10 square must be sqrt(200), or about 14.14 feet.

3/4/5 doesn't matter here.  Different triangle, different relationship.

Not really.  Lay out a 9x12x15 triangle to set the angle.  Shorten the 12 and extend the 9 to get the dimensions you really want.  If you don't think you can lengthen a side and keep it straight, stake out 12x16x20 and then measure 10 feet in each direction from the corner.
Title: Re: Math actually works!
Post by: AZRedhawk44 on August 14, 2019, 11:42:39 PM
Not really.  Lay out a 9x12x15 triangle to set the angle.  Shorten the 12 and extend the 9 to get the dimensions you really want.  If you don't think you can lengthen a side and keep it straight, stake out 12x16x20 and then measure 10 feet in each direction from the corner.

I completely grok that 3/4/5 is extensible to 6/8/10, 9/12/15, 27/36/45 ad infinitum.

Castle key wants a rectangle that is 10x60, segmented into 6 adjoining 10x10 squares, and to ensure that all square segments are perfectly square with 90 degree angles.

For a given 10x10 enclosure, you ensure that the corners are square by measuring the diagonals of the square.  Those diagonals create an isosceles right triangle.

If the diagonal from top left to bottom right is the same length as the diagonal from bottom left to top right, then you have a properly squared structure.

|\| = |/|

If those two diagonals are not equal, you don't have a square... you have a rhombus or a trapezoid or an irregular 4-sided structure.  But it ain't a square.

In the case of a 10x10 square, 3/4/5 has no relationship at all... but there is a well documented relationship similar to 3/4/5 that pertains to isosceles right triangles:  1/1/sqrt(2).

https://www.themathpage.com/aTrig/isosceles-right-triangle.htm
Title: Re: Math actually works!
Post by: zxcvbob on August 15, 2019, 02:21:49 AM
I completely grok that 3/4/5 is extensible to 6/8/10, 9/12/15, 27/36/45 ad infinitum.

Castle key wants a rectangle that is 10x60, segmented into 6 adjoining 10x10 squares, and to ensure that all square segments are perfectly square with 90 degree angles.

For a given 10x10 enclosure, you ensure that the corners are square by measuring the diagonals of the square.  Those diagonals create an isosceles right triangle.

If the diagonal from top left to bottom right is the same length as the diagonal from bottom left to top right, then you have a properly squared structure.

|\| = |/|

If those two diagonals are not equal, you don't have a square... you have a rhombus or a trapezoid or an irregular 4-sided structure.  But it ain't a square.

In the case of a 10x10 square, 3/4/5 has no relationship at all... but there is a well documented relationship similar to 3/4/5 that pertains to isosceles right triangles:  1/1/sqrt(2).

https://www.themathpage.com/aTrig/isosceles-right-triangle.htm

I understand what you're saying; did from the start.  And checking that the diagonals are equal is the sanity check to make sure your box is rectangular.  But you can use a 3/4/5 triangle to lay out the first right angle; (maybe you're in the field and can't remember the square root of 2  ;/) none of the sides have to be divisible by 3.  Mark off 3x from the corner in one direction, 4x in the other direction, and make sure the segment connecting those is 5x.

Once he has the 60' side staked out, put a flag every 10 feet.
Title: Re: Math actually works!
Post by: K Frame on August 15, 2019, 08:34:45 AM
Bob gets the concept.

Once you establish the right angle you have mother point.

You extend the right angle to set the other corner post of the narrow dimension (daughter) and the first post in the long side (son).

After that it's a tape measure and string line job to lay everything else out.

Getting the mother, daughter, and son posts set correctly is critical. One of those is out and everything else will skew.



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Title: Re: Math actually works!
Post by: K Frame on August 22, 2019, 05:38:10 AM
Talked to Castle Key the other day about this and it dawned on me, and no one here thought of it, either...

You make a story pole to set your poles. A very straight 2x4, a piece of iron pipe, whatever. Use it carefully and everything is set to the same distance apart.
Title: Re: Math actually works!
Post by: zxcvbob on August 22, 2019, 11:43:02 AM
Talked to Castle Key the other day about this and it dawned on me, and no one here thought of it, either...

You make a story pole to set your poles. A very straight 2x4, a piece of iron pipe, whatever. Use it carefully and everything is set to the same distance apart.

How is that easier than laying out the 60' side first with wooden stakes and a piece of string, then marking 10' sections on the string?  Unless the 10' measure is less critical than just having them all the same; then I guess it might be.

Triangulate the first 10' corner to get a right angle, using whatever is your favorite pythagorean triple. ;)  Use a 10' string and a 60' tape measure to locate the 4th corner, then check that the diagonals are the same and make any necessary minor adjustments at that 4th corner post because that's where any errors should show up.  Mark off 10' sections again.
Title: Re: Math actually works!
Post by: Hawkmoon on August 22, 2019, 11:45:42 AM
As we can see, there are probably as many ways of doing this as there are people laying out bocce courts.
Title: Re: Math actually works!
Post by: 230RN on August 22, 2019, 03:27:26 PM
....
Title: Re: Math actually works!
Post by: K Frame on August 22, 2019, 04:19:01 PM
A storey pole eliminates the creeping errors that can factor in when trying to make final adjustments before your concrete sets.

A tape flexes, kinks, bows out, all of which can throw your measurements off over distance. A storey pole doesn't.

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