02 Dot Product
... There are special unit vectors that point in the coordinate directions. The vector i points in the x-direction, j in the y-direction, and k in the z-direction. (The names change in more than three dimensions, so we won’t run out of letters!) Now let’s explore what happens when a dot product is zero ...
... There are special unit vectors that point in the coordinate directions. The vector i points in the x-direction, j in the y-direction, and k in the z-direction. (The names change in more than three dimensions, so we won’t run out of letters!) Now let’s explore what happens when a dot product is zero ...
Geometry Common Core
... Mathematics | High School—Geometry (taken from Common Core) An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts—interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or des ...
... Mathematics | High School—Geometry (taken from Common Core) An understanding of the attributes and relationships of geometric objects can be applied in diverse contexts—interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or des ...
Think of the game rock, paper, scissors
... • In the middle region, all shapes have 2 pairs of equal sides. Note that if a figure has 4 equal sides, then it also has 2 pairs of equal sides. But the converse is not true. • In the outermost region, figures have a pair of equal sides. In the universe are the figures with no equal ...
... • In the middle region, all shapes have 2 pairs of equal sides. Note that if a figure has 4 equal sides, then it also has 2 pairs of equal sides. But the converse is not true. • In the outermost region, figures have a pair of equal sides. In the universe are the figures with no equal ...
Pre-Algebra, Unit 1: Variables, Expression, and Integers
... Rule 4: When subtracting integers, change the sign of the problem from subtraction to addition, change the sign of the subtrahend (second number), and use rules 1, 2, or 3 for addition of integers. Another way to state this is “add the opposite”. Multiplication and Division Rule 5: When multiplying ...
... Rule 4: When subtracting integers, change the sign of the problem from subtraction to addition, change the sign of the subtrahend (second number), and use rules 1, 2, or 3 for addition of integers. Another way to state this is “add the opposite”. Multiplication and Division Rule 5: When multiplying ...
A geometric view of complex trigonometric functions
... of the non-negative imaginary axis and numbers with a positive real part (see Figure 3). In general, the complex distance between two points in C2 is a complex number (with non-negative real part). However, since any point wz on U satisfies z 2 + w 2 = 1, its complex distance from the origin of C2 ...
... of the non-negative imaginary axis and numbers with a positive real part (see Figure 3). In general, the complex distance between two points in C2 is a complex number (with non-negative real part). However, since any point wz on U satisfies z 2 + w 2 = 1, its complex distance from the origin of C2 ...
A = b
... Perpendicular bisector A line that divides a line segment in half and is at right angles (90°) to the line segment. Equal line segments are marked with “hash” ...
... Perpendicular bisector A line that divides a line segment in half and is at right angles (90°) to the line segment. Equal line segments are marked with “hash” ...
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 in a plane may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.