The chapter also presents the Pythagorean theorem, which states that in any right triangle, the square of the length of the longest side—called the hypotenuse—is equal to the sum of the squares of the lengths of the other two sides....
The Pythagorean theorem for Figure 1.1 is c2=a2+b2. Next, a set of useful trigonometric identities will be presented. The trigonometric unity is cos2θ+sin2θ=1. (1.4) The law of cosines is a very useful formula to know, and the geometrical setup is shown in Figure 1.2. ...
Harold E. Wolf, Introduction to Non-Euclidean Geometry , p. 63 for the term “hyperbolic geometry” and p. 144 for the traditional hyperbolic Pythagorean theorem (The Dryden Press, New York, 1945). A nice derivation of the traditional hyperbolic Pythagorean theorem is found in David C. Kay,...
In this introductory chapter, we shall present an overview of Euclidean Geometry in a general non-technical context. In the first section, a historical account of the origin of Geometry is presented along with its connection to Number Theory (Pythagorean Theorem, Fermat’s Last Theorem). In the...
The elusive character of Pythagoras is only one part of the problem. There exists a vast corpus of anonymous Pythagorean and Neo-Pythagorean literature, which bears all the hallmarks of religious scripture. More Pythagorean texts have come down to us than all the rest of the pre-Socratic philoso...
Introduction to number theory lecture 43 Gaussian integers (480 X 768) 36:00 Introduction to number theory lecture 44 Pythagorean triangles (480 X 768) 23:08 Introduction to number theory lecture 45 Dirichlet series (480 X 768) 31:04 Introduction to number theory lecture 46. Products of Dirich...
It is possible to determine the length of a vector from the coordinates using the Pythagorean Theorem. The image shows the vector represented by (2,3). Diagram showing the vector example. To determine the length of the vector, the Pythagorean Theorem states c2=a2+b2 So, the length of the...
The graph of - 5 is to the left of - 3, so - 5 is less than - 3, written as -5 < - 3. We can also write - 3 > - 5. Since - 3 is to the right of - 5, - 3 is greater than Martin-Gay, Prealgebra, 5ed The absolute value of a number is the number’s distance fr...
We need a way to find out the horizontal length (a) based on the information we’ve already got. And to do that we need to employ a basic formula from high school maths. You might remember the Pythagorean Theorem which shows the relationship between the lengths of the sides of a right...
(Note that we cannot use the Pythagorean theorem to add vectors that are not perpendicular. We will develop techniques for adding vectors having any direction, not just those perpendicular to one another, in Vector Addition and Subtraction: Graphical Methods and Vector Addition and Subtraction: ...