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  1. Between Arithmetic and Algebra - Cut the Knot!, Alexander Bogomolny
    What is the difference between the arithmetic 3+5 = 5+3 and the algebraic a+b = b+c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives expression to acknowledgement of patterns as such. How did people express general ideas before the advent of algebra in the 15th-17th centuries? A discussion of patterns and number systems with a Java applet showing Addition and Multiplication Tables in Various Bases. An interactive column for MAA Online that uses a Java applet to simulate a puzzle or mathematical problem, one not stated directly since the applet is intended to be such that the right answer to an as yet unstated problem should be easy to surmise. Also at http://www.cut-the-knot.org/ctk/between.html. more>>

  2. Patterns - Suzanne Alejandre
    Links to Web sites with patterns. Students look through the pages and answer these questions: How do natural patterns influence us? How do patterns help us to solve problems? Can you put elements of a pattern into an order that can be measured? that can be studied? that can be predicted? more>>


 

Mason error

error in file:   /usr/lib/perl5/5.6.0/Carp/Heavy.pm
 
line 79:  Bizarre copy of ARRAY in aassign
context:  
... 
75:  # them according to the format variables defined earlier in
76:  # this file and join them onto the $sub sub-routine string
77:  if ($hargs) {
78:  # we may trash some of the args so we take a copy
79:  @a = @DB::args; # must get local copy of args
80:  # don't print any more than $MaxArgNums
81:  if ($MaxArgNums and @a > $MaxArgNums) {
82:  # cap the length of $#a and set the last element to '...'
83:  $#a = $MaxArgNums;
... 
component stack:   /library/branch.html
/library/dhandler
code stack:   /usr/lib/perl5/5.6.0/Carp/Heavy.pm:79

debug info:   Debug file is '/var/lib/mason/debug/anon/9'.

raw_error





























raw error:
 






























error while executing /library/branch.html:
Bizarre copy of ARRAY in aassign at /usr/lib/perl5/5.6.0/Carp/Heavy.pm line 79.