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Looking for Examples of Math in Wodworking

4K views 58 replies 45 participants last post by  oldnovice 
#1 · (Edited by Moderator)
I just answered a question about figuring out an arc and this got me thinking about how math is used in woodworking. My daughter is going to start teaching high school math in a few weeks, in a charter school that is using project oriented teaching. My daughter is trying to pull together as much real-world examples as she can. In part to help combat the too commonly held belief that you never use math anyway, so why learn it.

Anyway, I'd appreciate any examples you can provide where you use math in the real world. Doesn't need to be restricted to woodworking, though that is in keeping with LJ.

I don't need lengthy details or diagrams, though if you have some specific formulas that would be great. But I do want them to be real examples. I can think up all sorts of things where I might use it. But as an engineer I use it where most people wouldn't bother.

Thanks in advance for any ideas and examples.
 
#2 ·
My background is in mechanical engineering of which some of can be carried over to wood working, specifically in calculating loads on members of a structure. Simpler structures like a wall in a house might be a better example than a curvy contemporary piece of furniture where the math can get quite a bit more complicated quickly.

What grade level will she be teaching?

The best example I can remember from early in high school was making scale truss bridges in teams using 1/8" square pine and dyed green wood glue. The objective was to use as little resources and have the maximum weight capacity when tested to failure. It wasn't so much about the math as the concept of keeping everything triangulated.

Later in high school in mechanical drafting and learning to draw an ellipse knowing only two dimension could be another application relevant if you were to make a elliptical table.
 
#5 ·
clin,

Your daughter is taking on a daunting challenge to convince high school kids that their education has significant value. Some will get it, but it seems in this day and age it is only after several years out of high school that they begin wishing they had taken their education seriously. I recall this very question from my kids; why do I have to learn all this stuff? They seemed impressed with my explanation but their commitment to school remained the same. Nonetheless I applaud her efforts and hope she succeeds.

Here are five pretty basic things derived from math, couched as questions. Most can be used in woodworking but obviously have wider applications.

1. I heard that the base of the pyramids in Egypt is distances evenly divisible by pi. They must not have had a long enough tape measure so could they have used a circle to measure distance? (geometry of a circle)

2. How did geologists come up with a diameter of the earth as 7,917.5 mi? (geometry of a sphere)

3. How do you pour a large concrete pad without the Pythagorean's theorem and its derived 3, 4, 5 or 6, 8, 10 rules? (geometry of a right triangle)

4. How much carpet is needed to cover my floor? (area)

5. How many board feet of lumber do I need to build a rectangular table top 1-1/2" x 3' x 6', allowing for 20% waste? (rectangular volume)
 
#6 ·
Common examples:

If I want to make a mitered square, what angle do I cut each piece at? What about a hexagon/heptagon/octagon, etc.

Using sine, cosine, tangent to calculate the angle of a cut from known dimensions, or an unknown dimension from a known dimension and a known angle.

If I want to make an oval/ellipse of a certain dimension, where do I place the foci of my jig to get what I want?

Using geometric principles to figure out angles of pieces that come together.

Caluclating volume of a piece, and using the density of the material to figure out the weight.

This is usually beyond highschool, but you can calculate the load/stress a bolt will be under to determine the diameter and or thread pitch bolt you should use.

-Brian
 
#7 ·
Figuring out gear ratios for clocks.

Creating different cuts of shellac.

Determining angles for adjacent staves in a multi-sided cylinder (barrel, or mast)

Costing out projects for fun or profit

Calculating volumes of concrete for piers or piles

Calculating power requirements for a circuit

I believe there is a strong correlation between understanding the logic of mathematics and good programming skills (Arduinos and Raspberry Pi platforms are affordable for classroom use)

I am sure there are more but I've had a long day on a construction project where I, ironically, used no mathematics at all except at the fast food joint calculating my change at lunchtime. :)
 
#8 ·
All the last posters were correct but maybe a bit too deep for them iff they dont have basic math skills already? Simple Fractions and Decimals, she may be taking on a fruitless/dauntless task. I commend her effort!!
So if they do have basic math skills, I have a 3×3' skid in the warehouse, I can only load it 3' high, how many cubic feet do I have? How many cubic yards?
I have to pour a concrete slab 3.5" thick by ?X? how many cubic yards of cement do I need?
I have a wall ?x? and I need to cover it in Tyvac wrap, the roll is 12' x 50', how many rowels do I need?
Building a wall X length with a 2×4 at each end and one every 16" how many do I need?
I have a Triangle 45 all sides, how many do I need to make a square object? a Rectangular one?
I have a triangle 30
x30x60 same question.
If I have a side of a roof 30' wide and horizontal to the ridge it is 16', how many square feet for a 1-4' pitched roof compared 1-6' pitched roof?
Mom sends you to the store for a Gallon of Milk, they are out of Gallons and only have Quarts, how many for a Gallon?
Mom needs a cup of Whipping Cream they are out but just have Pints, how much more did you buy?
I could go on for ever, God help your daughters sanity after a few weeks. I commend her effort!!
 
#13 ·
Wood working a Board foot, so I have a piece of wood 6" wide by 8 long x 1 " thick, how many Board Feet is that? 4.
I have 6"x 8×1.5" thick, how many Brd Ft is that? 4 but at a different price range.

- nightguy
nightguy
Your first example is correct…second example is 6 board feet, not 4.

OP
In addition to your example of determining the radius of an arc, some other basic geometry used in the stair industry for both straight and curved stairs…
Pi r2 or Pi D
a2 + b2=c2
Pretty basic stuff, but essential for a good stair builder, or rail installer and/or site measure and/or estimator.
 
#15 ·
When I worked as a sheet metal worker I often needed to know how long a duct was required to offset an certain amount at 45°, using 45° ells. I multiplied the offset by the square root of 2. (1.41) to get this dimension.
When making a round pipe I needed to know the total circumference of the wanted round duct in order to make it. C=pi d
Just two examples in working with metal..
 
#16 ·
Ask them to solve problems involving the most efficient way to build a particular item. For example - you have 3 pieces of 1×6x8 lumber and you wish to build a square coffee table. What are the max dimensions the table can be? Then take it a step further and have them try building a mini version of something using balsa wood, or maybe a full size version depending on the school's facilities.

I'm not great at math but I teach high school. Kids like to solve problems and they like when there are multiple solutions they can share with each other.

Good luck to your daughter.
 
#17 ·
relate maths to specific jobs to conect the how and the why

. Carpenter - measure to frame and roof house. make a box. make and fit window etc
. Blacksmith - work out the size of metal bar to cut off to make another object
. Pipefitter - how long to cut to form bends and strait runs.
. Chef - how much food and booze to buy how much to portion and how much to sell for including Food+ utilities+ taxes+ wages+ depreciation+ maintainance+ insurance+ repairs+ Permits+ licences+ Trash+ Bribes+ gifts+ Protection money etc
. Military - if you cant count you cant get in
. Lawn service - pricing cutting, fertiliser, weedkiller, hourly outlays (Truck, gas, tools Wages etc)
. slinging burgers at Mcdanalds - to check you wages so boss cant cheat you
 
#18 ·
The golden ratio: the convergence of the quotient of a fibonacci number divided by its previous term as the series approaches infinity. Roughly 1.618 to 1. A frequently used proportion in determining what is aesthetically pleasing, found in art, architecture, furniture, etc.
 
#19 ·
I have 14 stone tabletops to make for a restaurant. Each top is 3ft x 5ft. The stone that is specified for the project comes in 55"x122"x3/4" slabs. The material cost me $12.50 per square ft.

1. How many slabs do I have to order to complete the project?
2. How much will the slabs cost?
3. How much of the material will be un-useable waste?
 
#22 ·
Here are 2 formulas I came up with. I don't believe they are perfect formulas, but from my experimenting they come pretty close for me.
1st is a formula for finding the length of 1 side of a hexagon using the width.
Width divided by 1.732051615
Triangle Parallel Font Pattern Slope


2nd is finding a 22 1/2 deg angle using the width.
Width x .4142173 (add answer to width to determine distance to measure to for 22 1/2 angle)
Rectangle Slope Parallel Font Circle


Like I said, they are not perfect formulas. I find them to work very well with measurements up to a couple of feet but haven't tried them on a bigger scale.
 

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#23 ·
There's lots of math/arithmetic in just about any construction project or in making almost anything.

If you are going to build anything, you have to figure how much material to buy.

How many boxes of flooring? How many bundles of shingles? How many cubic yards of concrete? How many fence boards? How many board feet of lumber? How many gallons of paint?

I would start with those kind of questions.

Every day on Craig's List you see people trying to sell the extras after having bought too much for their project.

-Paul
 
#24 ·
Also, they need to have some sense of how to estimate things using simple math.

How many decimal places do need for a particular calculation?

When is 17 good enough as 1/6th of 100?

Being able to quickly estimate without a calculator gives you a way to check to see if your calculations are reasonable. This is a practical skill.

-Paul
 
#25 ·
The flaw here is that woodworking isn't a real world problem for high schoolers, anymore than roofing, warehousing, chemistry, stocking or any other thing adults do. If you want the kids to relate then the example needs to be from their world. But kids rarely need math so it's difficult to come up with real world examples that relate to them. I wonder if it wouldn't be more effective to give them the problem then teach them how to solve it vs teaching them how to solve it and then looking for a problem. Subtle difference but might work.
 
#26 ·
Thanks for all the input. This thread topic seems to be hotter than a "which table saw should I buy thread."

I know it can be tough to get kids attention when they don't need to use math in their world. The rent, cable, cell phone, car etc bills all get paid with all that easy money mom and dad make, doing whatever boring thing it is they do when they're at work. It is easy for them to not relate. Of course not relating to other peoples lives is something a lot of us adults do too.

It will be up to my daughter and the other education professionals to come up with how to connect with the students. But I thought I'd pick the forums brains and put together some examples for her to draw on if she thinks it will be useful.

Good or bad, she's starting in a very non-traditional school. Her own experience is in traditional classrooms, so she trying to understand how to teach math in this unusual school.
 
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