Cut the Knot
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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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!: 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!: 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.
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Cut the Knot: Proof Without Words
This site explains the method of proof using diagrams. The site gives some history of methods of proof and how it has changed through time. The site gives numerous examples of proofs without words and a practice exercise to be worked on...
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Cut the Knot!: Analogues and Generalization of the Pythagorean Theorem
This site discusses the theorems and other findings which are directly related to the fundamental Pythagorean theorem. Be sure to click on the link to information on Pythagorean theorem to find several proofs of the theorem.
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Cut the Knot!: Recipes for the "Average Value" of a Function
Site explains a "recipe" for finding the average value of a function using summations.
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Cut the Knot!: Fundamental Theorem of Algebra
Contains a summary of the fundamental theorem of algebra as it pertains to integrals.
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Cut the Knot!: Remarks on Proving the Fundamental Theorem of Algebra
Contains relevant information regarding to the fundamental theorem of algebra.
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Cut the Knot!: Proofs in Mathematics
This site provides an explanation of mathematical proofs. It also has links to different types of proofs.