Math Forum Internet News

Volume 3, Number 18

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 4 May 1998                                   Vol. 3, No. 18


Impossible Constructions | Searching Standards | Pascal's Triangle


Three geometric construction problems from antiquity puzzled 
mathematicians for centuries: the trisection of an angle, 
squaring the circle, and doubling the cube. Are these 
constructions impossible?

Read about these "impossible" constructions in the latest 
addition to the Dr. Math FAQ:

"Whether these problems are possible or impossible depends 
on the construction 'rules' you follow. In the time of 
Euclid, the rules for constructing these and other geometric 
figures allowed the use of only an unmarked straightedge and 
a collapsible compass..."

      Links to sites on the Web that offer discussions,
      investigations, and constructions using a marked 
      straightedge and other devices are also provided. 


                   SEARCHING THE STANDARDS


See how different states treat the same topics in their
Standards: Achieve offers a searchable database of statements 
of educational standards produced by states and national 
professional organizations.
Each document is identified by its source, the academic 
subject it covers, and the grade levels to which it applies. 
Searching by subject allows you to view all of the documents 
pertaining to a given academic subject, such as mathematics. 
A search by topic lets you choose one or more areas within 
a subject - for example, the topic of measurement within 
mathematics - and find only documents pertaining to those 

With a full text search, you can specify particular words
or phrases and find all the documents in which they appear. 

Achieve, Inc. is a Resource Center on Standards, Assessment, 
Accountability and Technology.




If you prefer, browse this annotated list of Internet sites
with K-12 mathematics educational standards and curriculum
frameworks documents, maintained by Charles Hill and the
Putnam Valley, NY schools. There are annotated links to ENC,
Explorer, McREL, NCTM and more than 35 states. Sites for
math education standards are listed by organization and by
state, and Canadian sites are also included.



           PASCAL'S TRIANGLE - a Math Forum Web Unit

Pascal's triangle is an arithmetical triangle made up of 
an unlimited number of staggered rows of numbers.

                              1 1
                             1 2 1
                            1 3 3 1
                           1 4 6 4 1

Many number patterns are found in Pascal's triangle, and it
is used in two major areas of mathematics: algebra, and
probability and combinatorics.

Read about the history of Pascal's triangle and learn to 
construct it; view illustrations of number patterns to be
discovered; carry out interactive investigations in Java
script or the Geometer's Sketchpad, and explore this famous
triangle through lesson plans that feature questions, answers, 
discussion, and student worksheets for students at the 
elementary, intermediate, and advanced levels:

Suggested Web sites and relevant Standards are also provided:


          TAPPED IN  - MATHEMATICS with Dave Kershaw


Monday, May 4 - 4:00 p.m. Pacific time; 7:00 p.m. in the East 

   Should teaching style depend on the teacher or the
   student? Do you change your style to meet a particular
   student's learning abilities, or is your style based 
   on what you can do?

The Math Forum brings its resources to TAPPED IN's 
professional development multi-user virtual discussion
environment. All grade levels are welcome. 

For questions about the discussions or using TAPPED IN, 
contact Dave Kershaw ( or 
Judi Fusco (


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