Trisection of angles-similarly

[DrRocket]

It would be better if he spent his time helping little old ladies across the road or, at least, trying to do something where he might succeed.

 

I am fond of some little old ladies and would prefer a more reliable source of aid.

[michel123456]

90° is feasable too.

 

Curiously, I was never interested in the question.

Yesterday I made a simple thought: it is possible to make a circle, draw 3 smaller circles (of random radius) upon its circumference, and create an arc, divided in 3 equal parts, forming a random angle.

I wondered why the reverse construction was impossible (beginning from the angle and dividing the arc). As if geometry had a direction that cannot always be reversed, like entropy and time...

 

Now I took some time to draw that.

 

Step 1. a circle.

 

Step 2. a smaller circle with a center on the circumference of the big circle.

 

Step 3. a 2nd small circle, identical, with center at the intersection of the 2 circumferences.

 

Step 4. segments joining the center of the big circle with the intersections on the circumference.

 

Step 5. erasing the circle, keeping the arc.

 

The angle is trisected, but there is no way to make the construction backwards. Isn't that remarkable?

Edited February 10, 2012 by michel123456

[imatfaal]

Yes - it is a nice construction and as you point out not reversible which is a shame and not unexpected. doG included a great link to a math profs page of quasi-trisections of an angle - repeated here . I think the various different failed/half-hearted attempts show how fascinating and doomed the quest is - and how close we can come even when we know it is impossible

Edited February 10, 2012 by imatfaal