# Category: Mathematics in Action

# Accuracy of Approximate Numbers

Mathematicians, especially those pursuing pure mathematics, prefer to work with exact numbers such as π , √2 , 5/7 . In the practical settings of measurement and computation, there is a need to approximate the actual value of a number, especially when a long or infinite decimal is involved. In order for such approximations to Read more about Accuracy of Approximate Numbers[…]

# Classical Geometry: Part 3

Here we consider a number of theorems concerned with the Euclidean geometry of the circle. We begin by reviewing some important structures related to the circle. Further Circle Anatomy The vital description of the circle in terms of its radius and centre may be found in The Shape of Things. The arc, a sometimes underestimated Read more about Classical Geometry: Part 3[…]

# Classical Geometry: Part 2

Triangle theorems

# Further Continuous Distributions: Part 2

Here we continue the treatment of continuous probability functions (distributions) begun in Probability Functions: Part 2 and Continuous distributions. Our emphasis is on distributions derived from the normal distribution. We begin with the Chi-square distribution, which was already considered in Further Continuous Distributions. But here we approach it as a sampling distribution. We then consider Read more about Further Continuous Distributions: Part 2[…]

# Continuous Distributions

This is an introduction to the probability functions of continuous random variables, from a post-secondary perspective. One of the most fundamental functions of this type is the normal distribution. Since it has been covered elsewhere, our main focus is on another fundamental continuous probability function, the uniform distribution. We close this essay by considering one of Read more about Continuous Distributions[…]

# Power Series

A power series is a polynomial of infinite degree. Thus it is similar in form to the general (degree n) polynomial, but has no last term:

# McLaurin’s Series

Let be a power series representation of f(x) within the interval of convergence |x| < r. That is, f(x) = It is easy to show that f(0) = a0. And, since f ‘(x) = , it follows that: and f ”(x) = Then it is easy to see that f ”(0) = 2a2 Read more about McLaurin’s Series[…]

# Samples and Sampling

As described in Statistics Defined, a sample is a set of raw data values drawn from a much larger source, the population. Purpose is …. Before drawing a sample, an investigator should clearly define the population from which it is to come. Outline of this essay … In order for a sample to be effective Read more about Samples and Sampling[…]

# Categorical data and the TI-84 Calculator

Our goal in this section is to illustrate how the TI-84 calculator can be used to perform tests on categorical data. Although the TI-84 is used in secondary schools, this topic is not normally covered at the secondary level in Canada. Example 1, genetic ratios (one-way table)…chi2cdf(0, chic, df) = .95 or .99 A more Read more about Categorical data and the TI-84 Calculator[…]