| Index to MATH.NOT 27-Jul-1984 (notes 1-100)
References to a main note (of the form x.0)
mean that the topic is discussed throughout
that note; so when investigating it, you
should peruse the responses to that note as
well. This index was produced by hand. A
complete concordance can be found in file
HARE::SYS$NOTES:MATH.CRD.
Topic References
----- ----------
120 degrees 22.0
1983 24.0
1984 24.0
3 inverters from 2 68.0
7-section 17.0
A/P 31.0
Absolute difference triangles 42.0
AI programs 20.2
algorithm design conference 82.0
algorithm for division 87.0
algorithm for reciprocal 87.0
alphametic solver 45.0
alphametics 45.0, 46.0
AMSTeX 43.0
approximations 56.0
Arnold Arnold 16.3
ASIN 27.0
backup datatypes 96.0
BCAL 15.0
Beyond Floating Point 23.0
Brent multiprecision package 26.0
British soldiers problem 69.0
bugs 89.0
calculus 34.0
CALX 15.0
casting out 9's 56.1
chain problem 40.0
chess problems 33.0
Clifford's theorem 20.3
coin problems 7.0, 55.0
Combinatorial Algorithms 5.0
complex log 32.6
complex polynomial 48.1
continued fractions 47.3, 57.4, 61.0, 98.0
convergent sequence 48.0
Conway, J. H. 10.0
counterfeit coins 55.0
curve fitting 85.0
curve in square 31.0
curve through 3 points 85.0
data analysis program 77.0
dice problems 97.0
difference equations 61.0
difference triangles, absolute 42.0
Difference triangles, distinct 14.0
differential equations 61.2
Digicalc 14.4
digital filters 36.0
disection puzzles 83.0, 84.0
Distinct Difference Triangle 14.0
doubly-true alphametics 46.0
duality 90.0
e, calculation of 92.24
equations from digits 24.0
error-correcting codes 6.1, 6.2
factorials 50.0
factoring 19.0, 21.0, 30.0, 49.0, 51.0
factoring programs 73.0, 81.0
factoring, algebraic 72.0, 94.0, 99.0
Fermat prime 17.1, 17.4
Fermat's Last Theorem 16.0
Fibonacci numbers 59.0
Fibonacci polynomials 94.0
firing squad synchronization 69.0
floating point 38.0
floating point package 47.0
foreign numbers 44.0
four fours problem 24.5
Frame formula 56.2, 56.4
generating functions 61.2
geometric duality 90.0
GOTO-less programming 5.1
graph theory 53.0
Guess a number 6.0
Hamming code 6.3, 6.5
handshaking 18.0
harmonic series 52.0
Heronian triangles 70.0
horizon calculation 56.3
IEEE floating point standard 38.0
IEEE library 36.0
IMSL 60.0, 74.0
index 100.1
integer sequences 93.0
integrals 25.0, 86.0
interest calculations 56.0
inverters problem 68.0
IXP 28.0
i^i 32.0
job scheduling 75.6
Johnson's algorithm 58.3
Joy of TeX 43.0
k-subset 5.0
lattice points 22.0, 31.6
league scheduling 75.0
LINPAK 60.0
LISP 57.5
LN01 13.1
MACSYMA 15.0
MASS-11 15.0
math package 60.0
Merten's conjecture 39.0
microvaxen 96.0
modulo problem 66.0
Morley's theorem 20.3
most wanted factorizations 51.6
MP 26.0, 92.17
MPSET 26.2
multiprecision package 28.0
muMATH 15.0
N-clusters 41.0
NAG 60.0
non-procedural programming 8.4
NSA 16.6
number systems 23.0
palindromic sequences 95.0
Partitions 5.0
Partitions, balanced 9.0
Pell equation 57.0
Permanent 5.0
Permutations 5.0, 58.0, 66.5
pi, 10000 digits 92.8
pi, approximation 37.0
pi, calculation of 92.0
PICOMATH 15.0
Pizza 17.0
platonic solids 90.0
point symmetric graphs 53.0
Pollard's rho method 81.6
polytopes 90.1
powers 29.0
powers mod M 66.0
pretty theorems 20.0
prime plus power of 2 64.0
Prime producers 10.0
Primes, 333...3 21.0
Primes, A.P. 4.0
primes, alleged generation of 16.0
Primes, Mersenne 2.0, 51.0
primes, probable 21.1
probability, conditional 63.0
Quacks 16.2
queens, non-attacking 33.0
radix representation 67.6
Ramsey theory 54.0
random numbers 81.5
random variables 63.1
reciprocals, algorithm for 87.0
recurrences 61.1
recursion for sqrt 2 67.0
repunits 49.0
rifles 69.0
right triangles, solving 56.2, 56.4
RISK 97.3
Roman numerals 12.0
round robin schedule 75.5
RTL math LIBRARY 96.0
RTL math manual 80.0, 88.0
Rules 1.0
SAC-2 15.0
Scales, spring 7.0
scheduling 75.0
seminars 23.0, 35.0
semiregular polyhedra 91.0
SLATEC 60.1
SMP 15.0
SNOBOL4 12.0
spheres, opposite of 62.0
Spherical Trigonometry 11.0
sqrt 2 67.0
squaring makes smaller 79.0
STAT 77.0
STR$DIVIDE 89.0
sum of squares 78.0
Summation 59.0
Symbolic Math 15.0
system III 74.0
tangents to two circles 65.0
TECO macros 92.1
temperature conversion 56.0
test data 81.0
Tetrahedron 11.0
TeX 13.0, 43.0
TexBooks 13.2
three-body problem 16.1
TK!Solver 15.0
Tower of Hanoi 8.0
trigonometric identities 71.0
trigonometric sums 59.0
USENET 76.0
VAXIMA 15.0
Welcome 1.0
what are the 2 numbers 78.0
x^2+y^2+z^2 72.0
Zeta function 3.0
|
| Open Problems [comments by S. Rabinowitz]
---- --------
As of 26-Jul-1984, the following problems are still open:
Note # description and comments
------ ------------------------
7. spring scale coin problem.
Solution will be published in the Monthly before long.
14. Distinct Difference triangles.
Not likely to be solved. Has been published in the James
Cook Mathematical Notes. We'll see if they have any luck with it.
Can some upper bounds be found? Peter and I have some upper
bounds; but the details are embedded in the code and scribbled
on a listing sitting in my office.
18. Handshaking problem.
Come on guys... This is an easy one.
22. 120 degree angle in 3D lattice.
Let's hit this with some compute power!
33. Combinatorial chess problems.
Not likely to be solved soon.
41. N-clusters problem.
I was at one of the New York geometry seminars. Paul Erdos was
speaking on unsolved problems in combinatorial geometry. He mentioned
this as a long unsolved problem. If Erdos can't solve it, I would
forget about it.
42. Absolute difference triangles.
Appears hard. Perhaps some more data would help.
53. Point symmetric graphs.
Jerry tells me this one stumped all the graph theory professors
at Yale.
61. Difference Equation.
I've solved the differential equation (by hand) but have been too
lazy to enter the computation. Anyhow, this was of no use
because the resulting function had an essential singularity at 0,
so I was unable to recover the Taylor series.
Sloane gives a reference to this sequence; but the reference
(EUREKA - The Journal of the Archimedean Society) is to an
obscure British journal that I can't find in any American libraries.
Can any readers locate this journal in their library?
66. Powers mod M.
Let's keep working on this one...
67. Recursion for sqrt(2)
Several people are still actively working on this, but I think
it's futile.
68. n inverters from 2
Peter and I have been discussing this privately, and have concluded
that you can invert 4 signals with 2 inverters using a circuit that
glitches. The original proposal allowed glitches. We have no
formal proof yet that you can invert n signals with 2 inverters.
There are feedback problems. How about someone with access to
a schematics editor and a circuit simulator to "build" the circuit
for us and simulate it to see if it works or not, for n=5?
70. Heronian triangles with one side twice another.
Let's use up some computes!
72. Factoring x^2+y^2+z^2
Leroy Meyers sent me a simple proof these couldn't be factored.
You should be able to prove it too.
83,84. Lynn's dissection problems.
I don't believe we have a definitive answer yet. Perhaps we never
will. Can anyone do better than the dissection we currently have?
94. Factoring Fibonacci Polynomials.
I recently learned that a change of variables will turn the
Fibonacci polynomials into the Chebyshev polynomials (of the second
kind) and I think lots is known about factoring Chebyshev
polynomials; but I'm still researching this.
95. Palindromic sequences.
Anyone care to generate more data?
|