From sommerduo@earthlink.net Wed Mar 27 16:29:52 2002 Received: from relay1.netnames.net (coumxnn02.netbenefit.co.uk [212.53.64.123]) by sanford.math.niu.edu (8.12.1/8.12.1) with ESMTP id g2RMTglB005241 for ; Wed, 27 Mar 2002 16:29:45 -0600 (CST) Received: from [207.217.120.122] (helo=pintail.mail.pas.earthlink.net) by relay1.netnames.net with esmtp (NetNames 3.14 1) id 16qLvI-0005ht-00 for feedback11@math-atlas.org; Wed, 27 Mar 2002 22:29:40 +0000 Received: from 11cust108.tnt1.philadelphia2.pa.da.uu.net ([67.242.19.108] helo=[10.0.1.2]) by pintail.mail.pas.earthlink.net with esmtp (Exim 3.33 #1) id 16qLso-0005xB-00 for feedback11@math-atlas.org; Wed, 27 Mar 2002 14:27:07 -0800 User-Agent: Microsoft-Outlook-Express-Macintosh-Edition/5.02.2022 Date: Wed, 27 Mar 2002 22:27:07 -0500 Subject: S3 From: michael sommer To: Message-ID: Mime-version: 1.0 Content-type: multipart/mixed; boundary="MS_Mac_OE_3100112827_218533_MIME_Part" X-Originally-To: feedback11@math-atlas.org Status: RO Content-Length: 317671 > This message is in MIME format. Since your mail reader does not understand this format, some or all of this message may not be legible. --MS_Mac_OE_3100112827_218533_MIME_Part Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Hello Dave, Here is a little something I cooked up which you may find fun. I play with the Sommer CUBE, i.e. S3, it in its physical as well as in its virtual mode( on the RayDream Carrara application). You will see, for example, that the eight cube configuration contains one cube containing four crossing passages, e.g. a quadruple path cube; this one is a nice little trick and very efficient. That is, a minimum number of cubes with maximum development. Of course there is no limit to the number of cubes which can be used or the length or configurations of pathways, unlike the Rubiks CUBE. And of course, each additional cube creates exploding combinations of failure. Also, unlike R3, S3 allows direct manipulation of the individual cubes, as well as introducing the problem of gravity. And there is something else: the manipulation of the individual cube is confusing; it is difficult to keep one's orientation in the decision space. I hope that you find the S3 interesting. >From the mathematical perspective, I have many questions, for example: Q. What is the minimum number of cubes necessary to make FOUR QUADRUPLE PATH CUBES, so that the ball(s) exits at the lowest cube level? Q. Using the criteria above, what is the maximum number of linked conduits possible? Q. Using the criteria above, what is the minimum number of conduits possible? Q. Now, let's say we use 27 cubes for the S3, the same number found in the R3. Are there more combinations possible in the R3 or S3? Remember, the law of gravity must be respected. Michael Sommer www.sommercube.com By the way, it is probably perfectly obvious that I am not a mathematican. If I were I would not have to build this cube but instead, create equations for it. If you could me understand what I am saying in mathematical terms I would be very grateful. m --MS_Mac_OE_3100112827_218533_MIME_Part Content-type: image/jpeg; name="@@cover to web ###### to copy 1"; x-mac-creator="6F676C65"; x-mac-type="4A504547" Content-disposition: attachment Content-transfer-encoding: base64 /9j/4AAQSkZJRgABAQEASABIAAD//gAMQXBwbGVNYXJrCv/bAIQABwUFBgUFBwYGBggHBwgK EQsKCQkKFA8PDBEYFRkZFxUXFxodJSAaHCMcFxchLCEjJygqKioZHy4xLSkxJSkqKAEHCAgK CQoTCwsTKBsXGygoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgo KCgoKCgo/8QBogAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoLAQADAQEBAQEBAQEBAAAA AAAAAQIDBAUGBwgJCgsQAAIBAwMCBAMFBQQEAAABfQECAwAEEQUSITFBBhNRYQcicRQygZGh CCNCscEVUtHwJDNicoIJChYXGBkaJSYnKCkqNDU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVm Z2hpanN0dXZ3eHl6g4SFhoeIiYqSk5SVlpeYmZqio6Slpqeoqaqys7S1tre4ubrCw8TFxsfI ycrS09TV1tfY2drh4uPk5ebn6Onq8fLz9PX29/j5+hEAAgECBAQDBAcFBAQAAQJ3AAECAxEE BSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNE 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