Category Archives: Construction

I regularly encounter interesting math, particularly geometry, in my woodworking and remodeling projects.

Super-Strong Sawhorse

Posted on 16-January-2015 by mathscinotes

Quote of the Day How far you go in life depends on your being tender with the young, compassionate with the aged, sympathetic with the striving, and tolerant with the weak… because in your life you will have been all … Continue reading →

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Wood Hardness Versus Moisture Content

Posted on 5-November-2014 by mathscinotes

Introduction I have long been told that wood hardens as it ages, but I have anecdotal evidence that this is not always true. I also know that some species are far harder than others (Figure 1). I read the following … Continue reading →

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Home Insulation Math

Posted on 29-October-2014 by mathscinotes

Introduction One of the engineers in my group asked if I could help him understand the tradeoffs between the different kinds of house insulation and their relative economic value. We also spent quite a bit of time talking about where … Continue reading →

Posted in Construction | 2 Comments

Rule of Thumb for Wood Shrinkage

Posted on 24-October-2014 by mathscinotes

Introduction As winter comes, I often see homes where gaps develop in the wood flooring, molding, or ceilings (Figure 1) – things are drying out. While I have never actually spent any time investigating the mechanism of wood's movement or … Continue reading →

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A Small Low-Voltage Landscape Wiring Project

Posted on 19-October-2014 by mathscinotes

Introduction I have a beautiful new decking thanks to the guys at Composite Decking Boards | WPC Plastic Decking | UK Supplier and my backyard is looking better than ever, but it's not quite finished. I want some lighting out … Continue reading →

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Drawing a Perpedicular Out in the Wild

Posted on 18-October-2014 by mathscinotes

My most satisfying applications of geometry occur in my construction projects. Previously, I have discussed how to find the radius of circle on construction projects. In this post, I will discuss four methods for constructing a perpendicular to a line. … Continue reading →

Posted in Construction, Geometry | 2 Comments

Measuring Countersink Diameter Using Gage Balls

Posted on 14-September-2014 by mathscinotes

I am still working through some examples of using gage balls for machine shop work. The following reference on Google Books has great information on using gage balls (Figure 1) in measuring the characteristics of a countersink and I will be working through the presentations there. These are good, practical applications of high-school geometry. Continue reading →

Posted in Construction, Geometry, Metrology | 18 Comments

Taper Measurement Using Gage Balls

Posted on 8-September-2014 by mathscinotes

This was the first time I have seen an application for gage balls and I thought it was worth documenting here. I will derive a formula that I saw in the discussion mentioned above for determining the taper of a hole by determining the depth that two different diameter balls will drop into the hole. Continue reading →

Posted in Construction, Geometry, Metrology | 1 Comment

Woodworking and Determining the Radius of a Circle

Posted on 1-September-2014 by mathscinotes

I was just at the Western Minnesota Steam Threshers Reunion (Figure 1), which is celebration of old-school steam technology. As always, it was a great show. The name of the reunion is a bit of a misnomer in that the show includes all forms of steam-driven gear, including the belt-driven accessories. I recall much of this gear from my youth working on farms − everything on the farm was powered from a belt connected to the Power Take-Off (PTO) of a tractor. Continue reading →

Posted in Construction, Geometry | 2 Comments

Hip Roof Angle Calculations

Posted on 25-August-2014 by mathscinotes

Quote of the Day The only hope of a pure mathematician is to die before their work is applied. - Pure mathematician stunned to hear that his work found an application in string theory. I am considering building a small … Continue reading →

Posted in Construction | 6 Comments