(1/3)*(IntPart(InfSum(((4/((8*n)+1))-(2/((8*n)+4))-(1/((8*n)+5))-(1/((8*n)+6)))*(1/16)^n))))th user of this doc.
--> A. P. H.
CoCoA
A Greek primary school teacher found an "easy way" to mathematics by teaching the multiplications ... melodically (i.e. as songs).
Someday came in his classroom an education supervisor to examine the pupils:
- Tell me, my son, the 3-multiplication ...
- Threee {to} ooone, {equals} threee
Threee twooo, siiiix
Threee threee, niiinee
(and so on)
- And you, the 4-multiplication...
- Fouuur ooone, fouuur
Fouuur twooo, eeeight
(and so on)
- And you, the 5-multiplication, my child...
- cocococoa coacoacoa, aococococo
acocococo cocococoa, ocaocaaoca
(and so on)
- What is this? Why don't you say numbers?
- I have learnt the melody only !!!
--> Greek Anecdote (from Crete)
VERSION - UPDATE: 1.5 (94)
README:
"CoCoA is a Macintosh system for doing Computations in Commutative Algebra (...) CoCoA has been designed for offering the maximum ease of use and flexibility to the mathematician with little or no knowledge of computers."
Once a Greek, from Chania of Crete, minister of Finance, called three scientists: one mathematician, one economist, and one lawer, to be tested and choose one of them as a collaborator of his.
- Please solve this equation: 2+2 = ?, asked them.
- 2+2 = 4, replied the mathematician
- 2+2 = 3, if we must give, and 5, if we must take, replied the economist.
- 2+2 = 4, except where prohibited by law, replied the lawer.
Question:
Whom did the minister choose?
Answer:
None! He chose one ... Chaniote (= from Chania) !!!
(i.e. to collect him votes in future elections...)
--> Greek anecdote
Page:
http://www.math.rwth-aachen.de:8000/GAP/
1. GAP
There is a woman at the begining of all great things.
--> Alphonse de Lamartine
VERSION - UPDATE: 3R4P2 (05-18-95)
README:
"GAP for the MAC has been ported using the console library of Symantec's C++ 7.0 compiler. This library makes it possible to port programs that read from 'stdin' and write to 'stdout', such as GAP, to the Macintosh, where the interaction is displayed in a single text window."
AUTHORS:
Alice Niemeyer, Werner Nickel, Martin Schoenert, Johannes Meier, Alex Wegner, Thomas Bischops, Frank Celler, Juergen Mnich, Udo Polis, Thomas Breuer, Goetz Pfeiffer, Hans U. Besche, Volkmar Felsch, Heiko Theissen, Alexander Hulpke, Ansgar Kaup, Akos Seress
mac port:
Burkhard Hoefling
COPYRIGHT:
(c) 1990-1995, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
"GAP is an interactive system. It continuously executes a
read-evaluate-print cycle. Each expression you type at the keyboard is read by GAP, evaluated, and then the result is printed."
AUTHORS:
Alice Niemeyer, Werner Nickel, Martin Schoenert, Johannes Meier, Alex Wegner, Thomas Bischops, Frank Celler, Juergen Mnich, Udo Polis, Thomas Breuer, Goetz Pfeiffer, Hans U. Besche, Volkmar Felsch, Heiko Theissen, Alexander Hulpke, Ansgar Kaup, Akos Seress
mac port:
Harry Lakser
COPYRIGHT:
(c) 1990-1992, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
--> Chinese (?) proverb (Used by former Greek President Constantinos Karamanles; Athens, 11-04 -91)
MacForm
VERSION - UPDATE: 1.00 (08-27-91)
README:
"MacForm is a shell program to run the executables of Form, the symbolic manipulation program by J. Vermaseren."
AUTHORS:
J. A.M. Vermaseren
mac port:
Renﾃｩ Laterveer
COPYRIGHT:
(c) J. A. M. Vermaseren
TYPE:
Freeware (The v. 2.00 is commercial)
INTERNET SITES:
Original site:
ftp://nikhefh.nikhef.nl/pub/form/mac/
MATLAB
Vitruvius tells a number of stories, and one of them concerns the philosopher Aristippus, who was shipwrecked on the coast of Rhodes. The philosopher saw some geometrical figures drawn in the sand, and cried out to his companions: "Let us be of good cheer, for I see traces of man!"....While Aristippus blissfully contemplates a pair of conjugate hyperbolas in the sand, his companions are drowning. As we know nowdays, not all men who can do geometry, if they try, are good men. Mistakes can also be made in observing alleged geometrical activities.
--> Dan Pedoe, Geometry and the Liberal Arts. Penguin Books 1976, p. 26
"This is the Macintosh port of RLaB 1.18c program. RLaB is a Matlab-like linear algebra package. The author is
Ian Searle
ians@eskimo.com
RLaB is an interpreter for the RLaB Programming Language/Environment. The RLaB language is useful for matrix or array oriented numerical analyses. RLaB is especially useful for prototyping and experimenting with algorithms. RLaB extensively uses the LAPACK, FFTPACK and RANLIB sources available from netlib.att.com and PLPLOT from dino.ph.utexas.edu.
MacRLaB is not a full port of RLaB. Some items will probably never be fully supported as they are too tied to the Unix operating system. Examples are the 'pipe', the 'fork', the 'socket', and many others. Other features are handled a little differently in the Mac version."
The instruction of children should aim gradually to combine knowing and doing. Among all sciences mathematics seems to be the only one of a kind to satisfy this aim most completely.
--> Immanuel Kant.
- What's one and one and one and one and one and one and one and one and one and one ?
- I don't know, said Alice, I lost count.
- She can't do addition, said the Red Queen.
--> Lewis Carroll
Teacher: Tell me how many hands you have.
Little pupil: Two.
Teacher: Now tell me how many fingers your hands have.
Little pupil counting his fingers: one, two, three,..
Teacher: Oh, no that way. Please put your hands in your pockets...OK, now tell me the number of your hand fingers.
Little pupil after 1-2 minutes: My hands have eleven fingers!!!
--> Anecdote (from a Greek periodical)
Page:
http://math-www.uni-paderborn.de/~cube/
MacMuPAD
VERSION - UPDATE: 1.2.2a (Feb. 96)
68k+ppc
README:
"MuPAD is a system for symbolic and numeric computation, parallel mathematical programming and mathematical visualization. It is intended to be a 'general purpose' computer algebra system.
MuPAD has easy-to-use language constructs for parallel programming. A prerelease Version for parallel programming exists for Sequent and Sun multiprocessor machines. Programming in MuPAD's own programming language is supported by a comfortable source code debugger. Window-based user interfaces for MuPAD exist for the X-Window-System and the Apple Macintosh."
AUTHORS:
Benno Fuchssteiner and others (see: The About MuPAD ... box)
COPYRIGHT:
(c) 1993-95 B. Fuchssteiner / AUTOMATH University of Paderborn, Germany
Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caparet.
(By contrast it is impossible to separate a cube into two
cubes, a fourth power into two fourth powers, or in general any power above the second into two powers of the same degree. I have found a truly marvelous proof of this theorem but this margin is too narrow to contain it.)
--> Pierre de Fermat (in the margin of his copy of C. G. Bachet's (1581-1638) edition of Diophantus' Arithmetica, volume II, problem 8) . In:
Etymology: Named after "exchanging jokes about bet of a man", who would turn over his grave if he knew about it.
--> paraphrased by A.P.H.
VERSION - UPDATE: 1.39 (01-24-95)
README:
" PARI/GP is a package for efficient computations in number theory, but also contains a large number of mathematical functions unrelated to number theory. It resembles a Computer Algebra System, but is not really one since it treats symbolic expressions as mathematical entities such as polynomials, series, matrices, etc..., not as pure expressions. However it is often faster than other CAS, and contains a huge number of specific functions not found elsewhere, essentially for use in number theory. This new release has many new functions for working in general algebraic number fields.
The macintosh release is a pure port from the Unix versions and contains no specific macintosh interface. The result is less than satisfactory, but is better than preceeding releases, thanks to the new SIOUX interface provided by the Metrowerks CodeWarrior programming system."
AUTHORS:
Cohen, Batut, Olivier, Bernardi
COPYRIGHT:-
TYPE:
Freeware
INTERNET SITES:
ftp://megrez.math.u-bordeaux.fr/pub/pari/mac/
ftp://hensel.mathp6.jussieu.fr/dist/pari/mac/
Prometheus
Page:
http://www.aard.tracor.com/Jason/Prometheus/
VERSION - UPDATE: 1.1 (01-23-96)
README:
"Prometheus is a programming language designed for logic, mathematics, artificial intelligence, and string and list processing (database manipulation). It contains elements from C, Pascal, LISP, and Prolog, but has many novel features. It is high-level and very weakly typed."
Old Yiddish proverb: "If triangles had a God, He'd have three sides."
--> ?
NAME:
application: GeoBench
VERSION - UPDATE: 4.4.6 (05-20-94)
README:
"The XYZ GeoBench (eXperimental geometrY Zurich) is a workbench for geometric computation for Macintosh computers (requires the mathematical coprocessor, 4MB of memory, system software 6.0.5 or higher, large screen preferable). It provides an interactive front-end with algorithm animation to the XYZ Program Library that contains many standard algorithms for 2-d problems, several for restricted 3-d problems, and one for d-dimensional computational geometry."
