+
Unit Plan
Cut the Knot

Cut the Knot!: Polygons: Formality and Intuition

For Students 9th - 10th
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...
+
Unit Plan
Cut the Knot

Cut the Knot!: Geometric Construction With the Compass Alone

For Students 9th - 10th Standards
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...
+
Activity
Cut the Knot

Cut the Knot! Pick's Theorem

For Students 9th - 10th
This site explains Pick's Theorem and contains an interactive geoboard and activity to help understand the theorem.
+
Unit Plan
Cut the Knot

Cut the Knot!: Napoleon's Theorem

For Students 9th - 10th
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...
+
Handout
Cut the Knot

Cut the Knot!: Pythagoras' Theorem

For Students 9th - 10th
This site explains the Pythagorean theorem, giving a proof from Euclid, and gives a great interactive visual aid with a good explanation with it.
+
Graphic
Cut the Knot

Cut the Knot!: Mathematics: The Science of Patterns

For Students 9th - 10th
A book excerpt, this page discusses John Venn's "simple, geometric method for checking the validity of syllogisms," with diagrams, examples, and related links.
+
Activity
Cut the Knot

Cut the Knot!: Monge's Theorem of Three Circles and Common Tangents

For Students 9th - 10th Standards
Very good site presenting a Trig problem dealing with tangents lines and circles, then linking the student to the solution
+
Activity
Cut the Knot

Cut the Knot: Lattice Multiplication

For Students 9th - 10th Standards
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...
+
Handout
Cut the Knot

Cut the Knot!: Note on the Extreme Value Theorem

For Students 9th - 10th
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
+
Activity
Cut the Knot

Cut the Knot!: Example of Convergent Infinite Series

For Students 9th - 10th
This site explains the sum of a simple convergent series using a geometric illustration.
+
Handout
Cut the Knot

Cut the Knot!: Math Glossary, Math Terms

For Students 9th - 10th
This site from Cut the Knot is a math glossary with hundreds of math term and links to explanations for each.
+
Website
Cut the Knot

Cut the Knot!: Interactive Mathematics: Geometry Articles, Theorems, Problems

For Students 9th - 10th
Contains over five hundred Geometry articles, problems, puzzles, and games. Some sites relating to circles are provided within this list.
+
Unit Plan
Cut the Knot

Cut the Knot!: Napoleon's Theorem

For Students 9th - 10th
This site gives an explanation of Napolean's Theorem and gives several links to Napoleon's Theorem.
+
Unit Plan
Cut the Knot

Cut the Knot!: Shapes of Constant Width

For Students 9th - 10th
Description of what constant width means along with the question "are there shapes of constant width?". [Requires Java.]
+
Activity
Cut the Knot

Cut the Knot!: The Law of Cosines (Cosine Rule)

For Students 9th - 10th Standards
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.
+
Activity
Cut the Knot

Cut the Knot: Proof Without Words

For Students 9th - 10th
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...
+
Handout
Cut the Knot

Cut the Knot!: Analogues and Generalization of the Pythagorean Theorem

For Students 9th - 10th
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.
+
Handout
Cut the Knot

Cut the Knot!: Recipes for the "Average Value" of a Function

For Students 9th - 10th
Site explains a "recipe" for finding the average value of a function using summations.
+
Unit Plan
Cut the Knot

Cut the Knot!: Fundamental Theorem of Algebra

For Students 9th - 10th Standards
Contains a summary of the fundamental theorem of algebra as it pertains to integrals.
+
Unit Plan
Cut the Knot

Cut the Knot!: Remarks on Proving the Fundamental Theorem of Algebra

For Students 9th - 10th Standards
Contains relevant information regarding to the fundamental theorem of algebra.
+
Website
Cut the Knot

Cut the Knot!: Proofs in Mathematics

For Students 9th - 10th Standards
This site provides an explanation of mathematical proofs. It also has links to different types of proofs.