# Those Handy Maths Formulars



## Grumpy (Nov 9, 2007)

I will start this one off Jocks. Partridge posted a forum topic on a maths problem http://lumberjocks.com/topics/2954
Following I thought it would be a good idea to start a forum on maths formulars and calculations for the benefit of all Jocks.
Many of us know the 3-4-5 rule for triangles which comes in very handy in woodwork. gator9t9 raised this one.You can construct a triangle of any size in that 3-4-5 proportion and it will be accurate. 
I will start with the problem of finding the area of an irregular triangle when you know the lengh of the 3 sides but not the angles.

*Area of Triangle*
Area = √[s(s-a)(s-b)(s-c)] 
where s=1/2 the perimeter & a,b&c are the lengths of the 3 sides.
Ok Jocks, lets see what else you have stored in the memory cells.


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## GaryK (Jun 25, 2007)

I don't do math. I do AutoCAD.


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## swied (Feb 6, 2008)

A golden rectangle has sides with a ratio close to 5:8. If you want be exact make it 11+sqrt(5))/2

Supposedly, this is the most eye pleasing rectangle.


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## TroutGuy (Mar 28, 2008)

My favorite is (and always will be): 8 + 2 = 10. Then (and ONLY then), 5:00 + 10 = Miller Time!

Here's one that took a bit of research. Find the angle between two faces of any regular pyramid.

cos(A) = *-* ((R^2 + (2 *x* H^2+R^2) *x* cos(t))/(2 *x* H^2 + R^2 + R^2 *x* cos(t)))

Find the arccosine and you're done!

Note: I had to play with the formatting a bit, to get the formula to display correctly. LJ kept 'interpreting' my multiplication asterisks as formatting commands, which changes parts of the formula to *BOLD*, AND leaves out the asterisks. Does anybody know how to suppress the auto formatting, temporarily?

Anyway,

A= the angle between the faces (the number I needed)

and I knew

R= the distance from the center of the pyramid's base, to the vertices
H= the height of the pyramid
t= the angle (in deg) between the bases of adjacent pyramid faces (t=360/n where n= the number of faces - e.g. for a hexagonal pyramid, t=60 deg)

This works for any 'regular' pyramid, regardless of size, or number of faces-think gazebo roof. I got tired of punching the numbers into a calculator, so I put the formula into an Excel spreadsheet. Enter those three pieces of info, and it calculates the rest.

If you'd like a copy of that Excel file, let me know.

The formula came from, http://mathforum.org/library/drmath/view/55203.html. They explain this more better than I can.


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## douglas2cats (Mar 31, 2008)

I just usually consult one of the numerous math related links I've saved. If I cant find what I need there, then I dust off my rusty trig/calculus and commence to cyphering with my gazintas ala Jethro.
http://www.intmath.com/
http://www.csgnetwork.com/sawmitercalc.html
http://www.woodweb.com/knowledge_base/Radius_of_Convex_Wall.html
http://johnmcgaw.com/wwsoft.html
http://www.jsommer.com/WoodMath/WoodMath.html
http://www.ajdesigner.com/phptriangle/equilateral_triangle_inscribed_circle_radius_r.php


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## robdew (Mar 25, 2008)

I can never remember how to calculate the dimensions of a jig to use with a router template. That is, how much bigger to make the outline to be cutout.

It's something like the the difference between the outside diameter of the template ring and the bit, halved?


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## Suz (Feb 12, 2008)

Here is a website that has a calculator for almost anything you have to crunch numbers for.

http://www.martindalecenter.com/Calculators1A_5_Co_RZ.html#HOMER-WOODW-BOOKSHELF
This is just the wood calculator section, there are over 23,465 calculators available!

Then if you go to the main reference page, there are thousands of other references.

http://www.martindalecenter.com/


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## LeeJ (Jul 4, 2007)

Opps;

I think I'm on the wrong site!

Lee


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## Toolz (Feb 26, 2008)

Son:" Dad Pi r square" 
Dad: " No son Pi are round cornbread r square"

Seriously folks I have marked this thread as a favorite. Thanks


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## Grumpy (Nov 9, 2007)

Tremendous Jocks & great links as well. what about the simple ones that the tradesmen use to take short cuts. there must be heaps out there.


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## Boardman (Feb 7, 2008)

I do appreciate the links, since I'm not an advanced math person. I think it goes back to high school, where I had a geometry teacher that we nicknamed Froggy. One day I brought in a picture of a frog with the teacher's face cut out of the yearbook and pasted over the frog's head. Yup….I got busted with it.

On one site I saw this inetresting question - "Why Study Analytic Trigonometry? "

I can't think of any reason at all…....


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## SDL683 (Oct 15, 2011)

heres a math question.
i suck at math… so heres a question i have.
If i take a 90 degree square surface thats 2" square. and i want to cut one corner flat to 3/4" wide
how far back on the sides do i make my mark???


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## Eli (Mar 3, 2010)

The radius of a circle is the same length as 1 side of an inscribed hexagon (one where all the points are on the circle). So if you set a compass to the radius, and walk it around the outside of the circle, it will break it into a hexagon.

Also, if you draw an inscribed right (all the points on the circle, one corner is 90 degrees) triangle in a circle, the hypotenuse (long side) always crosses through the center of the circle. Either find the center of the hypotenuse to find the center of the circle, or draw two of them and the lines will cross in the center.

The angles of a triangle always add up to 180 degress. You can take a polygon (a closed shape with some number of straight edges) and break it into triangles, then multiply the number of triangles by 180 and it will tell you how many degrees are in your shape. If your shape is regular (all of the angles are the same) then you can divide the degrees by the number of corners and it tells you what angle all of the corners are.

Eli


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## CharlieM1958 (Nov 7, 2006)

Silas: I think the correct formula would be A sq. X B sq. = C sq., with C = 3/4".

But if you've got a combination square, who needs all that math? Just slide the 45 degree side of the square along one edge until the distance across the graduated side is 3/4".


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## MrRon (Jul 9, 2009)

I remember when I went to school, way way back, kids would say; "all this math stuff won't do me any good later in life". I'm not a mathematician, but I'm glad I paid attention in class. I still do most math in my head, only using a calculator when working in decimals or converting English/Metric. I now realize how important a subject like Mathematics is, not just for the mathematicians, but for everyday use for you and me. Those of you with school age children; impress upon them how important it is to know their math; language also.


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## BillWhite (Jul 23, 2007)

You'd be amazed at the number of young folks who can't even read a tape measure. Scary!!!!
Bill


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## DrDirt (Feb 26, 2008)

Always found it amusing that struggling with math is accepted and common stand-up comedy.
Imagine the difference if folks instead were saying "I never really got that reading thing back in school" it just isn't as funny.

True it is rare to need calculus - but seems algebra and geometry keep popping up regardless of chosen profession.


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## 33706 (Mar 5, 2008)

I knew a dental hygienist who thought she had no need to study calculus, but alas, that is exactly what she ended up removing from her patients' teeth.


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## zzzzdoc (Mar 6, 2010)

My favorite. For those who like limericks:


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## rance (Sep 30, 2009)

My favorite math problem is 342-173


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## CharlieM1958 (Nov 7, 2006)

Okay zzzdoc… you challenged me, but I think I have it:

Twelve plus one hundred and forty-four
Plus twenty plus three times the square root of four
Divided by seven
Plus five times eleven
Equals nine squared plus nothing more.


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## zzzzdoc (Mar 6, 2010)

Close. Very close.

A dozen, a gross, plus a score.
Plus three times the square root of four.
Divided by seven.
Plus five times eleven.
Is nine squared and not a bit more.


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## donjohn24 (Oct 15, 2010)

At last an excuse to get someone to look here: http://www.donjohnson24.co.uk/puzzle.html LOL

Its an arithmetic problem but needs a fair amount of logic to get the solution.

Set by my maths lecturer when I was at technical college over 50 years ago.


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## MrRon (Jul 9, 2009)

This goes waaay back, but merchants used to tally up a shoppers purchases with a pencil on the brown paper used to wrap the purchase. The package was then tied with twine. The shopper had all the numbers in his/her head in case the merchant tried to add in a penny or two.


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## DrDirt (Feb 26, 2008)

Thales Theorem I use quite often - but I just do the Physical layout - not the calculation

http://www.mathopenref.com/constcirclecenter2.html

Easy to find the center of a circle using a framing square, or any right angle that is handy - corner of a business card, dollar bill depending on the size of the circle.


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## richgreer (Dec 25, 2009)

I'm a little surprised to see a topic that is over 1200 days old become active again. Nonetheless I will add my 2¢.

I have an advanced math degree and i spent my entire professional career working in a heavily math oriented profession. I am a retired actuary.

I have no fear or math and no desire to utilize alternative means to avoid the need for math. I am totally comfortable in my ability with math, including trigonometry, and I use it quite often to solve for the right angle for a cut.

I assume that, in this regard, I am the exception. I just want to make the point that there are a few of us who use and enjoy using our math skills in woodworking applications.


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## Grandpa (Jan 28, 2011)

I can draw a perfect circle using a framing square. Ever see that done? select the diameter. drive 2 nails on that diameter. begin with the inside of the square on one nail and the pencil in the corner. slide the leg of the square over the other nail and the corner will move to the second nail and you have half the circle. Hard to explain but it works every time. 
Anyone ever use KAHN Academy. This is a great site for the mathmatically challenged.


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## Grumpy (Nov 9, 2007)

What would we have done without Pythagoras?. A bit of good old maths in woodwork keeps the brain active.


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