From shlomif@iglu.org.il Sat Oct 28 22:02:54 2006 From: Shlomi Fish To: "Hackers-IL" Subject: Rotating Objects Through the 4th dimension Date: Sat, 28 Oct 2006 22:02:54 +0200 User-Agent: KMail/1.9.4 MIME-Version: 1.0 Content-Disposition: inline Status: RO X-Status: RSC Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Message-Id: <200610282202.54669.shlomif@iglu.org.il> X-KMail-EncryptionState: N X-KMail-SignatureState: N X-KMail-MDN-Sent: Hi all! This is a small mathematical diversion I've thought of introducing here for a long time. I once read a book of mathematics that made the following proposition: if we take the following two triangles: ___ ___ ___/ | | \___ ___/ | | \___ ___/ | | \___ / | | \ *---------------- ----------------* then in a two-dimensional world they'll not be considered congruent (or "Hofefim" in Hebrew) because they cannot be rotated on the plane to match. In order for them to match one has to rotate them through the third dimension which is perpendicular to the entire plane. Now I've been thinking, since our objects are three dimensional, what would happen if we rotated them through a fourth dimension and back? Take those two objects for example: http://www.shlomifish.org/Files/files/images/Computer/Math/ (flip-thru-4th-dim-*.png). One of them is a cone that has an orthogonal cross-shaped extension on its middle side, and an orthogonal cylindrical extension 90 degrees counter-clockwise. The other has the cylinder 90 degrees clockwise. Now, in a three dimensional space, these shapes cannot be considered equivalent. But can we rotate one through a 4th dimension to form the other one? I hope to pick the brain of some of this list's mathematicians. Regards, Shlomi Fish --------------------------------------------------------------------- Shlomi Fish shlomif@iglu.org.il Homepage: http://www.shlomifish.org/ Chuck Norris wrote a complete Perl 6 implementation in a day but then destroyed all evidence with his bare hands, so no one will know his secrets.