In mathematics, a constant is a value that does not change. It is a fixed and well-defined number or quantity. Constants are used in mathematical expressions, equations, and formulas to represent known values that remain the same throughout a problem or calculation.

There are several types of constants in mathematics:

**Numerical Constants:**These are specific numerical values, such as 3.14 (pi) or 2.71828 (e).**Physical Constants:**These are mathematical representations of physical quantities, such as the speed of light (c) or the gravitational constant (G).**Mathematical Constants:**These are special numbers that arise in mathematical contexts, such as the golden ratio (φ) or Euler's constant (γ).**Universal Constants:**These are constants that have universal significance in scientific and mathematical calculations, such as the Planck constant (h) or the Boltzmann constant (k).

Some common examples of constants in mathematics include:

- The value of pi (π) ≈ 3.14159
- The base of the natural logarithm (e) ≈ 2.71828
- The speed of light in a vacuum (c) ≈ 299,792,458 meters per second
- Avogadro's number (N
_{A}) ≈ 6.022 × 10^{23}particles per mole

Constants are used in mathematical expressions and formulas to represent fixed values that are known and do not change. For example, in the formula for the area of a circle, the constant π is used:

Where r is the radius of the circle and π is a constant value representing the ratio of the circumference to the diameter of a circle.

When studying constants in mathematics, it is important to:

- Understand the concept of a constant as a fixed and unchanging value.
- Recognize and memorize common mathematical constants, such as π, e, and physical constants like the speed of light and gravitational constant.
- Learn how to use constants in mathematical expressions and formulas, and understand their significance in various mathematical and scientific contexts.
- Practice solving problems and equations that involve constants to reinforce understanding and application of these values in mathematics.

Understanding constants is fundamental to many areas of mathematics and science, and mastering their use can greatly enhance problem-solving abilities in these disciplines.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.