Trisect A Line With a Compass, Straight Edge, And Marking Device

[William McCormick]

This is pretty cool you can actually trisect a line with just a compass and a straight edge. It was in an old book I had, I mean like really old.

You just swing two arcs up to form the large triangle, then bisect the sides and you have the center point, then just swing two arcs the length of the midpoint of the height of the will be little triangle and get a thirty degree side of the smaller triangle. It is pretty cool, all you need is a compass and a straight edge or even a string, and of course a marking device.



I have some others for making circles inside of circles pretty cool stuff.



Sincerely,

William McCormick

[William McCormick]

This is pretty easy but cool.



Sincerely,

William McCormick

[William McCormick]

This is six circles in a cirlcle. All these are done without a tape measure or protractor.



Sincerely,

William McCormick

[William McCormick]

Dave, would you concur? That it can be done with just a compass/dividers, a string or straight edge, and a marking device?

You would not even need a square.

Sincerely,

William McCormick

[tapwelder]

That is interesting. in the first sketch, It is also a pictorial/proof representation of how/why you can take a line/rule of known length/division(blue) and divide a line of unknown length (Green).

Even shows similar triangles and how the divide the green line.

Lots of ways to torture young geometry students and have parent calling admin claiming irrelevance.

[William McCormick]

That is interesting. in the first sketch, It is also a pictorial/proof representation of how/why you can take a line/rule of known length/division(blue) and divide a line of unknown length (Green).

Even shows similar triangles and how the divide the green line.

Lots of ways to torture young geometry students and have parent calling admin claiming irrelevance.

Oh yea you can just use the old variable increment on an angle and do the same. But I thought that was pretty cool.

Sincerely,

William McCormick

[bent]

Way to much work. Draw a second line at an angle below the first, with the same starting point. Say at 30 to 45 degrees to the first, and about half again to twice as long. Now set your compass to a distance about 1/4 to 1/3 the length of the second line, and divide the second line. You don't have to be accurate as to meeting the end of the second line, anything short is useful. Draw a line from the last compass point on the second line to the end of the first line. Now draw two lines parallel to the end point line, intersecting the points found when you stepped off the second line with your compass. This divides your first line into three parts.

The good thing about this method is it works for any number of divisions, limited only by the size and neatness of your technique.