Cut the Knot
Cut the Knot!: Fundamental Theorem of Algebra
Contains detailed historical information regarding the Fundamental Theorem of Algebra and the various proofs that were developed. Click on the links at the bottom of the page to access all the information.
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Cut the Knot!: What Is a Number?
Casual and clear but definitely upper-level discussion of rational, real, imaginary, and several other types of numbers. Links to related sites.
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Cut the Knot!: Mathematics as a Language
A sophisticated discussion on the language of mathematics, its origins, meanings, and precision.
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Cut the Knot!: Polygons: Formality and Intuition
This is a very interesting site about polygons. The site begins by distinguishing between shapes whose sides intersect and polygons whose sides do not overlap. After this short introduction, you will find information regarding area and...
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Cut the Knot!: Geometric Construction With the Compass Alone
This site explains the possible uses of a compass when drawing. There are numerous exercises for using a compass with links to the solutions - click on the red checkmarks for these. The site discusses mathematicians who contributed to...
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What's a Rational Number?
This question is answered by discussing and comparing rational and irrational numbers. For more advanced levels of Algebra, there are sections that discuss different lemmas of rational numbers and give their proofs.
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Cut the Knot: 3 Glasses Puzzle
Challenge students to a well-known riddle involving three different-sized glasses, some water, and a goal of a certain amount to be measured out. At this site, students can actually "pour" the water back and forth to solve the problem.
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Cut the Knot: Probability Questions
This site defines probability and has a computer-based random number generator. The site has links to more than 100 probability problems which require some prior statistical knowledge to solve, or they can be great "openers" for teachers...
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Cut the Knot: Geoboard
Students can use the interactive geoboard to create different types of quadrilaterals and investigate the properties of quadrilaterals. Requires Java. The geoboard can also be downloaded for offline use.
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Cut the Knot! Pick's Theorem
This site explains Pick's Theorem and contains an interactive geoboard and activity to help understand the theorem.
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Cut the Knot!: Napoleon's Theorem
Site that describes in detail Napoleon's theorem. To understand this site be sure you understand what the centroid of an object is. The site describes polygons in terms of the roots of unity of a function. The page gives an interactive...
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Cut the Knot!: Pythagoras' Theorem
This site explains the Pythagorean theorem, giving a proof from Euclid, and gives a great interactive visual aid with a good explanation with it.
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Cut the Knot!: Mathematics: The Science of Patterns
A book excerpt, this page discusses John Venn's "simple, geometric method for checking the validity of syllogisms," with diagrams, examples, and related links.
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Cut the Knot!: Monge's Theorem of Three Circles and Common Tangents
Very good site presenting a Trig problem dealing with tangents lines and circles, then linking the student to the solution
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Cut the Knot: Lattice Multiplication
Have you heard of the 13th century mathematician, Leondardo Fibonacci? See examples of his concept of a lattice multiplication algorithm. Several example problems, including an interactive one where students can change the factors, are...
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Cut the Knot: Eight Digits Puzzle
Challenge yourself to this tricky little puzzle in which the player must position 8 digits in a pattern without having any paths connecting successive digits.
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Cut the Knot!: Note on the Extreme Value Theorem
This is a very good site defining the extreme value theorem and related theorems. The site has numerous links to topics related to the extreme value theorem
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Cut the Knot!: Example of Convergent Infinite Series
This site explains the sum of a simple convergent series using a geometric illustration.
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Cut the Knot!: Math Glossary, Math Terms
This site from Cut the Knot is a math glossary with hundreds of math term and links to explanations for each.
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Cut the Knot!: Interactive Mathematics: Geometry Articles, Theorems, Problems
Contains over five hundred Geometry articles, problems, puzzles, and games. Some sites relating to circles are provided within this list.
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Cut the Knot!: Napoleon's Theorem
This site gives an explanation of Napolean's Theorem and gives several links to Napoleon's Theorem.
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Cut the Knot!: Permutations
This page defines permutations, offering both mathematical definitions and examples and a practical explanation of how permutations are used.
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Cut the Knot!: Shapes of Constant Width
Description of what constant width means along with the question "are there shapes of constant width?". [Requires Java.]
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Cut the Knot!: The Law of Cosines (Cosine Rule)
This site from Cut The Knot provides an overview of the law of cosines, complete with an explanation of the law and a proof of the law.