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The wonderful (satirical, but mathematically sophisticated) book Mathematics Made Difficult introduces difference tables, and uses them to demonstrate how to co
by osteele 17y ago
The wonderful (satirical, but mathematically sophisticated) book Mathematics Made Difficult introduces difference tables, and uses them to demonstrate how to compute the next number in the sequence [1,2,4,8,16,…] – that number being, of course, 31.
This answer is correct in that it is the next item in the lowest-order polynomial that generates the first five terms. This reveals both the strength and weakness of difference tables (and the flavor of Mathematics Made Difficult).
- g__ 17y agoThis answer is also correct in another way :) http://threesixty360.wordpress.com/2008/04/30/1-2-4-8-what-comes-next/ http://threesixty360.wordpress.com/2008/04/30/1-2-4-8-what-c...
- jacobolus 17y agoHow does that work? Like this? That's not really following the "pattern" though, which is to keep adding 1 down the left edge of the triangle. Choosing to put a 0 in because we ran out of terms in our series is pretty arbitrary. 1 2 4 8 16 31 1 2 4 8 15 1 2 4 7 1 2 3 1 1 0
- req2 17y agoDifference tables don't operate on a "pattern"- they simply take the difference of the two terms above.
- jacobolus 17y agoNo, but the point is that using a difference table to find the "next term" in a sequence is rather stupid if the difference table doesn't terminate until you run out of terms.... the implication of that is that you have a sequence which cannot actually be fully described via that difference table.