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Geometry

Math Review of Representing Solid Figures

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Overview Three-dimensional solid figures can be represented by the two-dimensional pattern of polygons that create them. The pattern, called a net, is a visual representation that illustrates the formula for the surface area of the three-dimensional figure. If the net were folded, it would produce that figure. Representation of Cylinders The net for a cylinder…

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Math Review of Slopes of Parallel and Perpendicular Lines

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Overview Lines representing graphs of linear equations have slopes, defined as the change in y/change in x. Parallel lines have the same slope, but no solutions in common. Perpendicular lines intersect at one point to form right angles. Finding Slopes of Parallel Lines Imagine a line graphing the equation y = 2x +3. Using the…

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Math and Physics Review of Ice Hockey

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Overview In the winter sport of ice hockey, players, sticks, and the puck all move at a rapid pace. Sports scientists know that the apparent chaos of the game is governed by math and physics principles such as laws of motion; angles, vectors; transfer of potential energy to kinetic energy; and force, impulse, and collision.…

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Math and Physics Review of Football

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Overview The matchup between NFC West Champion Seattle Seahawks and AFC East Champion New England Patriots promises thrilling gridiron action during Super Bowl XLIX. Behind the scenes, principles of math and physics determine the shape of the ball itself, the running game, the passing game, and the kicking game. Footballs and Ellipses Many sports from…

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Math Review of Volume and Surface Area

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Overview Solid objects have both volume and surface area. Formulas for calculations can be expressed using algebra, especially if the measurements of sides are stated by variables. The ratio of volume to surface area is important in applications in chemistry and biology. Measurement of Volume The volume of a solid is the amount of space…

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Math Review of Triangle Inequality

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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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Math Review of Applications of Radical Expressions with Right Triangles

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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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Math Review of Roulettes and Cycloids

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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 Review of Platonic Solids and Polyhedra

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Overview There are infinitely many regular polygons. However, there are a fixed number of regular polyhedra, called Platonic solids. Mathematicians use the definitions of the regular polygons and the characteristics of solid objects to arrive at their conclusions. Characteristics of Regular Polyhedra Regular polygons, such as equilateral triangles, squares, equilateral pentagons, hexagons, heptagons, octagons, and…

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Math Review of More Fun with Tau

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Overview The quantity represented by the Greek letter tau (6.283185…) is the proportion of the circumference of a circle to its radius. The use of tau simplifies the relationships between angles and circles. These relationships underlie other branches of mathematics and applications to science. Special Angles and Tau The relationship of tau and the circle is…

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