I’ve heard people say ‘What good are learning things in school if you don’t use them?’. After my lifetime of careers, I realize you never know what may be useful to you later. One of my most useful high school classes for example, was a one-semester class in typing – a ‘fill-in’ course – way back when they taught ‘Typing’. I guess it is called ‘keyboarding’ if anything similar is even taught today.
Geometry was another, which at the time I studied it I could see no practical use for. But, as it turns out I used geometry in practice a great deal in my boatbuilding career, particularly in layout work. Thank goodness, enough of it stuck over the years to be very useful.
Case in point: Dividing a Line (or space) into equal parts;
Sometimes you need to divide a line, space or length into a number of smaller parts, all equal to each other. For example, suppose you have a space or piece of material 27-7/8” long which you need to divide into five equal parts. You can do this mathematically and end up with each part needing to be exactly 5.575” long. But, now you must convert this into English measurement equivalents (inches and fractions) and then try to measure these divisions with your ruler or scale. This is very hard to do accurately. Oddly, many common dimensions are hard to divide using English measures – for example 24” by 5 or 7 (4.8” & approx. 3.43”).
(And, let me say right here as an aside, that even though I have lived with English measurements all my life, things are much easier using metrics! Among all nations, only Burma, Sierra Leone and the US have never officially adopted the international metric system . . . ! That being said, you CAN buy ‘engineers’ scales which divide English measurements into tenths, but few besides engineers and machinists use those.)
But, back to my example; in three steps, you can quickly and easily divide any length by any number of divisions graphically using simple geometry. For those who are not familiar with this, I present it to you here:
1. Establish (draw) lines at either end of your length or space to be divided, and at right angles (perpendicular) to it. See image #1.
(Image 1 – space to be divided)
2. Place your ruler or scale between the two perpendiculars and angle it until you have a measurement you can easily divide by the number of equal spaces needed. For Instance, in the example above, you can easily use 30” and divide that by 5” increments to get 6 equal divisions. (Or, by 7-1/2” increments for four divisions, by 5” for six divisions, by 1” for thirty divisions and so on.) See image #2 & #3.
(Image 2 – make tic marks at dividing points)
(Image 3 – tic mark at each dividing point)
3. Mark these points (I always use a short line against the scale with a tic mark at the point for accuracy), and lines drawn at right angles from the original line (or space), through your points gives the equal divisions. Saw cuts centered on these lines will make exactly equal parts if you are sufficiently careful. See image #4:
(Image 4 – draw perpendicular from each point back to line or space being divided)
If you need to divide a plank into a number of equal widths, you may use either edge of the plank as your ‘perpendiculars’. Slant your scale and divide across from edge to edge at each end of your plank, and lines drawn with a straight edge through matching points will divide the plank into equal widths. A little thought shows you can even lay out a number of exactly equal tapers by adjusting the length of one end point! See image #5.
(Image 5 – laying scale at an angle between lines to make the divisions equal)
Hopefully, the pictures provided describe this well enough to understand.
-- "Never let your dogma get run over by your karma!"