| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
The problem is to find a closed-form expression for the sum:
n
D = Sigma [ k R ]
n k=1
Where brackets denote the floor function, and R is the 'golden ratio'
-- the positive root of x� = x + 1, or (1+sqrt(5))/2, or 1.618....
David Zeitlin has conjectured that if
S = [ (R n� + (R-1) n + 1) / 2 ]
n
then |D - S | <= 1.
n n
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 619.1 | CLT::GILBERT | eager like a child | Mon Dec 08 1986 23:09 | 23 | |
Let
A = (R n� + (R-1) n) / 2
n
Then
A - D = 1.7105572822+
6677056 6677056
and
A - D = -1.6341640721+
9829534 9829534
Thus, we see that Zeitlin's conjecture cannot be true, and that the looser
conjecture:
If S = [ (R n� + (R-1) n)/2 + g ], for some constant g
n
then |D - S | <= R.
n n
is also false.
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