# Ch 21: Well-Known Equations

### About This Chapter

## Well-Known Equations - Chapter Summary

Reintroduce yourself to widely-used theorems and formulas from the likes of Pythagoras, Newton, Euler, and Fermat. The informative lessons include the following topics for your review:

- The Theory of Relativity
- The Pythagorean Theorem
- Pi as it relates to circumference and diameter
- The formula for the force of gravity according to Newton
- Euler's Identity
- Fermat's last theorem
- Quadratic formula

The lessons in this chapter offer clear definitions and examples to accompany your practice. Listen to each video, or read the transcript, if you'd rather. At the end of each lesson, you can take the quick, multiple-choice quiz to see how you're doing. If there's anything that isn't clear, you can use the helpful video tags to go back and find that portion of the video right away. If you'd rather, you can just watch the entire video a second time.

### Regents Examination in Algebra I (Common Core) Objectives

This test checks to see that high school students are learning sufficient math concepts to prepare for college. It assesses your progress in four areas, including algebra, functions, number and quantity, and statistics and probability. You'll answer 24 multiple-choice questions and 13 constructed-response questions within three hours. The multiple-choice items have four possible answers from which to choose, just like our own online quizzes, which give you targeted practice for test day.

### 1. Theory of Relativity: Definition & Example

Einstein's special theory of relativity explains how energy and mass are related and how objects seem to behave as they approach the speed of light. Learn to define Einstein's theory of relativity, and use examples to explain the speed of light and Einstein's mass-energy equivalence equation and how it is used.

### 2. Pythagorean Theorem: Definition & Example

Pythagorean theorem, named after the mathematician Pythagoras, shows the relation between the sum of the squares of each of the three sides of a right triangle. Learn about the definition of the Pythagorean theorem, discover how a right triangle and sides of a triangle are used in the equation of the theorem, and explore the application of the Pythagorean theorem through relevant examples.

### 3. The Value of e: Definition & Example

The mathematical constant e was coined by the 18th-century Swiss mathematician, Leonhard Euler. Learn the definition of the value of e, what makes e an irrational number, and study an example of e.

### 4. Diameter and Circumference Related with Pi

In mathematics, pi is a constant that is equal to approximately 3.14, though the number actually is infinite. Learn about the definition of pi and explore its relationship to the diameter and circumference of a circle, the formula for calculating circumference, and also practice finding the circumference or diameter of a circle.

### 5. Isaac Newton's Formula for the Force of Gravity: Definition & Example

As the man who created the law of universal gravitation, Isaac Newton is one of the most renowned scientists to ever live. In this lesson, explore the definition of the force of gravity, the relationship of two objects, Newton's formula for the force of gravity, and an example of finding the force.

### 6. Euler's Identity: Definition & Example

As a famous mathematical equation, Euler's identity is often referred to as a mathematical jewel. Learn the definition of Euler's identity, explore why it is important, and discover how to apply the formula of Euler's identity formula with a provided example.

### 7. Fermat's Last Theorem: Definition & Example

Fermat's Last Theorem asserts that the sum of two positive numbers taken to a power greater than 2 will be equal to a third positive number taken to the same power greater than 2. Learn the definition of Fermat's Last Theorem, which was discovered in the margins of a book and remained unsolved for more than 300 years, and see how it relates to the Pythagorean Theorem.

### 8. Calculating Monthly Loan Payments

For most loans, such as a mortgage loan to purchase a house, the lender requires the borrower to make monthly loan payments, which include payments on the interest charged for the borrowed money. Explore the formula to calculate the amount of monthly interest and the number of payments required to repay a loan. Use the formula to find the monthly payment amount.

### 9. The Absolute-Value Inequality: Definition & Example

Absolute value inequalities are types of problems that may seem complicated from the outset but are relatively simple to solve with the right understanding. Take a closer look at the definitions of the absolute value and the absolute value inequality, followed by an example of how to set up and solve these types of problems.

### 10. The Quadratic Formula: Definition & Example

The quadratic formula is arguably one of the most well-known and important formulas in math. In this lesson, look at the definition of the quadratic formula, its standard form, how to plug in your values, and an example of the formula in action.

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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course

- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Overview of Functions
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Graphing Functions
- Calculations with Ratios, Percent & Proportions
- Understanding Sets
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Intro to Trigonometry
- Measurement for Algebra Students
- Geometry for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards