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4 May 1998 Vol. 3, No. 18 THE MATH FORUM INTERNET NEWS Impossible Constructions | Searching Standards | Pascal's Triangle IMPOSSIBLE CONSTRUCTIONS - Dr. Math FAQ 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: http://mathforum.org/dr.math/faq/faq.impossible.construct.html "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 NATIONAL CLEARINGHOUSE DATABASE OF STANDARDS - Achieve http://www.achieve.org/achieve/html/clearinghouse/main.html 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 areas. 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. http://www.achieve.org/ \|/ DEVELOPING EDUCATIONAL STANDARDS - Math 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. http://putwest.boces.org/StSu/Math.html -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- PASCAL'S TRIANGLE - a Math Forum Web Unit http://mathforum.org/workshops/usi/pascal/ Pascal's triangle is an arithmetical triangle made up of an unlimited number of staggered rows of numbers. 1 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: http://mathforum.org/workshops/usi/pascal/pascal_lessons.html Suggested Web sites and relevant Standards are also provided: http://mathforum.org/workshops/usi/pascal/pascal.links.html http://mathforum.org/workshops/usi/pascal/pascal_standards.html -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- TAPPED IN - MATHEMATICS with Dave Kershaw http://www.tappedin.org/ 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 (kersh@mathforum.org) or Judi Fusco (fusco@tappedin.sri.com). -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problems of the Week http://mathforum.org/students/ Internet Resources http://mathforum.org/~steve/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ |

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