Divide and Conquer
June 9th, 2007
Yesterday, Zohar Gilboa, with whom I take a PDE course, asked me the following riddle. I must admit it is probably the riddle I like the least on my site thus far. It is very easy though, and as Zohar told me he really liked it himself, I decided to publish it anyways.
Consider the following image:
Your goals are:
- Divide shape 1 (bluish) to two equal parts.
- Divide shape 2 (greenish) to three equal parts.
- Divide shape 3 (yellowish) to four equal parts.
- Divide shape 4 (purplish) to five equal parts.
All the division parts mentioned should be continuous shapes.
The second page contains the solution! Please only visit it after giving the riddle some thought…
Pages: 1 2
June 27th, 2007 at 11:23 pm
Funny.. I looked for a real solution for (4) – AKA geometric solution…
) but that should be proven
I believe it is not possible actually (using our B2 knowledge
July 1st, 2007 at 12:29 am
it sounds like you claim 4 is impossible, Ronnie – did you understand you correctly?
July 2nd, 2007 at 3:20 pm
Yes. I am saying it’s impossible to build it without a using a measuring device, such as a compass- only a straight ruler.
but I could be wrong, this is just my intuition.
July 2nd, 2007 at 10:04 pm
Oh, i misunderstood you then – i thought you said task 4 is impossible by any means – which as you guess, would be quite surprising… I didn’t take B2, so i can’t really claim to understand that intuition…
July 5th, 2007 at 9:46 pm
well.. I’m sorry:)
Anyway, if it interests you, I saw Yaniv published a review of this subject on “Constructions with a Straight-Edge and a Compass)”. I haven’t read it but it would probably provide insight on this problem.