Did cavemen care about geometry?

January 26, 2007 10:28 AM

Is there a way to get a perfect right angle out in the woods (for example)?

This came about because I started wondering how the very first right angle was formed. If you were out in nature with no tools (other than what you found lying around), could you make or observe a perfect 90° angle somehow? Perhaps using the sun? Or some rocks maybe?

posted by ORthey to Science & Nature (19 answers total)

If you have even so much as a stick, with which you can drag out a circle, then you can create the perpendicular bisector of a line - hence creating a perfect right angle.

For example.
posted by Wolfdog at 10:30 AM on January 26, 2007

Use the 3-4-5 rule.
posted by Joe Invisible at 10:36 AM on January 26, 2007

Another (admittedly, closely related) method.
posted by Wolfdog at 10:36 AM on January 26, 2007

you don't need to go quite that crazy and bisect anything - you just need a circle with the center marked. draw a diameter (any diameter!) and use that as one side of a triangle with the third vertex anwhere else on the circle's circumference. that third vertex will always be a right angle.
posted by noloveforned at 10:38 AM on January 26, 2007

yah, what wolfdog said ;)
posted by noloveforned at 10:39 AM on January 26, 2007

I believe using what Joe Invisible was suggesting - a rope divided into bits of length 3, 4 and 5 units and making the triangle, is what people like the Egyptians used to do.

Britannica link and there'll be lots more out there.
posted by edd at 10:40 AM on January 26, 2007

'Course, a rope divided into bits of length 3, 4, and 5 is one of the things that, traditionally, you don't have on your person out in nature. The problem's easy if you're carrying a T-square, too.
posted by Wolfdog at 10:43 AM on January 26, 2007

Yeah, what they said.

You can construct a "compass" by anchoring a vine or rope and using that to make circles.

Your "straightedge" can also be a vine or rope, held taut between two anchors.

One you have those basic tools, you can go crazy.
posted by vacapinta at 10:46 AM on January 26, 2007

Some rocks fracture in near-right angles, depending on their crystalline structure and how they are formed. Slate is an example that immediately popped into mind.
posted by muddgirl at 10:47 AM on January 26, 2007

'Course, a rope divided into bits of length 3, 4, and 5 is one of the things that, traditionally, you don't have on your person out in nature.

Maybe, but in the woods it would be really easy to make something like this out of sticks, grasses, or anything that is easily subdivided.
posted by blue mustard at 10:51 AM on January 26, 2007

Just take four straight sticks, and cut/sand/abrade them down so that they are all the same length. Then lay them down in a square shape. Use a fifth stick to measure the diagonals and adjust until both diagonals measure the same length. Now you have four perfect right angles.
posted by Rhomboid at 10:58 AM on January 26, 2007

Best answer: Standing water.

String (long piece of grass, whatever) tied to a rock.

Hold the other end of the string over the water, and the water will be perpendicular to the string.
posted by Kirth Gerson at 11:04 AM on January 26, 2007

Also, some crystals are cubes
posted by Kirth Gerson at 11:09 AM on January 26, 2007

Your quality of right angles will depend on how straight a line you can get. If you can get a rope or string, you're set. (Since you're probably be wearing woven clothes in the wilds, you've got some.)

Either use the string and two sticks to scribe out circles as Wolfdog pointed out, or coil the rope so it makes five loops, and mark it where the ends meet. You'll have the rope marked out in 5 equal segments which you can then use to do the 3/4/5 triangle bit. Or just use one stick as a measure and draw the line taut and measure stick lengths along it to get your 3/4/5s.
posted by Ookseer at 11:14 AM on January 26, 2007

Response by poster: Whoa, these are awesome answers. Consider yourselves all 'best answered.'

I'm going to try many of these on my next camping trip, which I believe makes me a huge dork.
posted by ORthey at 11:51 AM on January 26, 2007

Response by poster: Kirth Gerson, your rock and water one seems so far like the most precise right angle.
posted by ORthey at 11:55 AM on January 26, 2007

Discovering the 3-4-5 rule depends on having a right-angle to begin with.
posted by KirkJobSluder at 12:15 PM on January 26, 2007

If you have string or a straight stick, just dangle it over a calm pool. The surface of the water and the stick/string will be at a right angle.
posted by fvw at 12:52 PM on January 26, 2007

KirkJobSluder: not if your name is Pythagoras. More seriously, it is - like the other geometrical constructions - a consequence of mathematics and not having already got a right angle to compare it to.
posted by edd at 6:05 PM on January 27, 2007