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Math Review of Triangle Inequality 150 150 Deborah

Math Review of Triangle Inequality

Overview Students can connect algebra to geometry by expressing geometric inequalities in compound inequality form. Since the sum of the lengths of any two sides of a triangle is greater than the length of the third side, there are three inequality statements. All three inequality statements must be true for three line segments to form…

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The Physics of Spinning Objects 150 150 Deborah

The Physics of Spinning Objects

Overview Any spinning object rotates around a central point called an axis. Tops, dreidels, gyroscopes, and spinning eggs rotate, rise, and seem to defy gravity, as long as they are moving. When they stop moving, they fall. Angular Momentum Angular momentum refers to movement in a circle rather than a straight line. Imagine the movement of…

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Math Review of Factoring Trinomial Squares and Differences of Squares 150 150 Deborah

Math Review of Factoring Trinomial Squares and Differences of Squares

Overview Trinomial squares are also known as perfect square trinomials, and are the squares of binomial expressions. They factor as (a + b)(a + b) or (a – b)(a – b) where a and b are real numbers. Forms such as (a + b)(a -b) are special products that are also called the difference of…

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Math Review of Applications and Problem Solving for Rational Equations 150 150 Deborah

Math Review of Applications and Problem Solving for Rational Equations

Overview Rational equations have many applications to real-world problems. Some of the types of problems that can be solved include geometric ratios, number problems, motion problems, and work problems. Geometric Ratios When solving geometric ratios, it helps to use the problem-solving strategy of making a sketch to check against and see if the answer makes…

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Math Review of Applications of Radical Expressions with Right Triangles 150 150 Deborah

Math Review of Applications of Radical Expressions with Right Triangles

Overview The relationship of the length of the legs of the right triangle to the hypotenuse is expressed by one of the most famous equations in geometry, the Pythagorean Theorem. Deriving the measurement of the sides of the right triangle was one of the earliest uses of irrational numbers. Right Triangles Right triangles have one…

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The Measurement of Parallax: Angles We Have Seen on High 150 150 Deborah

The Measurement of Parallax: Angles We Have Seen on High

Overview The demonstration of parallax is as close as an observer’s own two eyes. It is the measurement of how the same object appears from two different points of view. Astronomers use the very small angles observed by parallax to estimate distances and relative motion of objects ranging from the sun, moon, and planets to…

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Math Review of Leibniz, Newton, and the Development of Calculus 150 150 Deborah

Math Review of Leibniz, Newton, and the Development of Calculus

Overview One of the biggest controversies in science in the early 18th century was around the development of a new mathematical tool called calculus. In Europe, the mathematician, philosopher, and scientist Gottfried Leibniz held the attention of the scientific community. The most famous scientist of the day, Sir Isaac Newton, was the champion of Great Britain.…

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The AC Method of Factoring Polynomials when A Is Not Equal to 1 150 150 Deborah

The AC Method of Factoring Polynomials when A Is Not Equal to 1

Overview The AC-method, also known as factoring by grouping, is often used to factor polynomials when the a coefficient is equal to 1. It can also be used when the a coefficient is not equal to 1, similar to the FOIL method. Questioning the Polynomial Expression The first step to defining the polynomial expression, before…

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Math Review of Roulettes and Cycloids 150 150 Deborah

Math Review of Roulettes and Cycloids

Overview Roulettes are special types of curves that are made when one curve is rotated around another by a fixed point. They are in Euclidean space, and can be described by calculus equations. Roulettes, cycloids, and other variations of circular movement have applications to pendulums, gears and subatomic particles. General Definition of a Roulette A…

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Math Introduction to Infinitesimals 150 150 Deborah

Math Introduction to Infinitesimals

Overview Using infinitesimal quantities to approximate measurement of any item is an ancient way to determine the size and shape of irregular objects. Although it was very controversial in the 17th and 18th century Europe, the practical aspects of using infinitesimal quantities in calculations led to advances in science, engineering, and technology, along with the…

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