# RE Pythagoras Style

Author: Dave
Date: 06.11.10 - 6:46pm

RE and hacking is at its base the ability to deduce the truth from a reality before you. Truth once known, means you can correctly intutit/extrapolate/predict other behaviors/relationships and often are able to manipulate it (within its limits) to the task you desire.

For ancient geometry guys..the most important RE of their day was that of discovering relationships of geometrical sizes and shapes. Fundemental to this analysis is the concept of measurement. Inches, Meters, the size of the unit is irrelevant. Consistent units is all that matters in reality.

Did you know the golden gate bridge is 720 giraffe necks long?

Those ancient dudes were actually brilliant in their simplicity. Or maybe they were unencumbered by all of our current day complexity.

Today I had to draw something to scale, I didnt have any graph paper or even a ruler, however i was able to draw it to scale quite accurately using an old school technique. relative units.

To start with, I drew a straight line about the scale i wanted for the project. It was to represent 40 feet. Then using dividers from a tech drawing set, I adjusted them until i could walk the line creating 4 segments. Now each segment represents 10 feet accurately. Divide 10 into 2 segments to see how long 5 ft is etc.

There is some margin for error because of line width on small units, but there is error margins in every single instrument we use and hey were roughing it here.

Now i did have a protractor for the angles which is good, but I didnt have to do any trig, I could figure out the elevations pretty well using the divider to step the distances.

Anyway, the reason i mention this, is it still kinda tickles my brain to see old simple techniques be quite accurate without all the complexity of modern tools and techniques. I feel like old school simplicity and intutive techniques are very lost in the modern engineering world. a lot of engineering students i went to school with trusted numbers implicitly. If they made a math error, they wouldnt have had the common sense to realize they were very much under-designing some structural component. No real world experience and intution to balance the numbers. Where as the old school techniques are based on observations, reality and deduced by intution.

Another old school technique i love in the mechanical realm is the methodology for precisely bolting parts together. If you dont have a cnc machine to layout the hole patterns on the individual parts, you would have to make some very accurate measurements by hand. Depending on the tolerances required you can get yourself in trouble if you try to drill them seperatly and hope for an alignment latter. but if you mark the holes on one piece, then clamp them both togehter in proper alignment, drill and tap one, bolt them together. drill and tap the next then bolt. You can assure perfect alignments of the pieces even on complex assemblies.

I learned these techniques in my early 20s when I built a Gingery style metal shaper from my own aluminum castings. Worked well then building a complex precision machine with very limited precision tools (dial calapers only)

The same techniques still served we well a couple years ago when i built a CNC Router and Plasma cutting table and now again today as I used a similar technique for creating a to scale representation of a problem i was trying to figure out.

I just get a kick out of RE and working with the tools at hand, no matter how limited they may be. In a world of computer control and precision down to the .0001 inch, sometimes we get lost in the complexity and fail to stop and realize that gross measures and relative measurements in non-units are just as valid for many many tasks. Just a random reminder of the simple side of life our modern society tends to shun in favor of the complex.

One other note i verified my expected numbers with some trig to see what my percentage of error was between the dividers and protractor. My trig calculated height elevation came out to be 8.6 feet, and my dividers calculated height was 8.75. At teh scale i was working, this difference equated to a pen line width for a 40 line at 20deg elevation. Not to shabby at all.

On 06.12.10 - 6:53pm Dave wrote:
 One more interesting bit i tested today out fo curosity. With only a compass, you can accurately replicate any angle you want using the same trick. Draw a circle, then use the compass as a divider and experiment until you can walk the circumference exactly with as many divisions as you want. (ie 4 divisions 90deg each, 660 etc.) Then you can divide each in half to get their halves, or 3rds etc. so 6-60, 3/60-20, 5/20-4, 4/4-1deg. and you have your own precision protractor created with nothing but a compass.

On 08.07.10 - 9:00pm Dave wrote:
 this has lead me to what looks to be a very interesting book A Beginners Guide to Constructing the Universe the authors personal site is here and you can find a radio interview of him here

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