machine shop calculation
... (6) Improper Fraction. This is a fraction having a numerator that is equal to or greater than its denominator. It is either a whole number or a whole number and a fraction of another whole number. For example, 4/4 may be expressed as 1, or 3/2 may be expressed as 1 + 1/2. (7 ...
... (6) Improper Fraction. This is a fraction having a numerator that is equal to or greater than its denominator. It is either a whole number or a whole number and a fraction of another whole number. For example, 4/4 may be expressed as 1, or 3/2 may be expressed as 1 + 1/2. (7 ...
How do you compute the midpoint of an interval?
... also intensively used in many numerical methods such as root-finding algorithms with bisection. It is, therefore, paramount that its floating-point implementation at least verifies Eq. (2). Accuracy, as stipulated by Eq. (3), is also desirable. Nevertheless, we will see in Section 3 that most formul ...
... also intensively used in many numerical methods such as root-finding algorithms with bisection. It is, therefore, paramount that its floating-point implementation at least verifies Eq. (2). Accuracy, as stipulated by Eq. (3), is also desirable. Nevertheless, we will see in Section 3 that most formul ...
doc
... In many cases, what is known is the length of only one side, plus the size of the angle involved. In these cases, use a scientific calculator to compute trigonometric ratios such as tangent from the angle size. This is very easy once you figure out just how the trig functions work on your particular ...
... In many cases, what is known is the length of only one side, plus the size of the angle involved. In these cases, use a scientific calculator to compute trigonometric ratios such as tangent from the angle size. This is very easy once you figure out just how the trig functions work on your particular ...
manembu - William Stein
... expressed as a simple continued fraction. He also provided an expression for e as a continued fraction, which he used to show that e and e² are irrational. Lambert generalized this work to show that ex and tanx are irrational if x is rational. He also proved the convergence of the continued fraction ...
... expressed as a simple continued fraction. He also provided an expression for e as a continued fraction, which he used to show that e and e² are irrational. Lambert generalized this work to show that ex and tanx are irrational if x is rational. He also proved the convergence of the continued fraction ...
Exercise 1
... 5.5.1. Warning: In order to prove the fundamental theorem of arithmetic we usually use Euclid’s algorithm and Bezout’s Lemma. Thus, when proving claims about Euclid’s algorithm (e.g. in the exercises above) we cannot use the fundamental theorem of arithmetic. 5.5.2. Remark: Although finding the grea ...
... 5.5.1. Warning: In order to prove the fundamental theorem of arithmetic we usually use Euclid’s algorithm and Bezout’s Lemma. Thus, when proving claims about Euclid’s algorithm (e.g. in the exercises above) we cannot use the fundamental theorem of arithmetic. 5.5.2. Remark: Although finding the grea ...
Document
... Find the are of the triangle formed by the points ( p + 1, 1 ) , ( 2p + 1 , 3 ) & ( 2p + 2 , 2p ) and show that these points are collinear if p = 2 or ½. 7. If the distance between the points (0,y) and (8,9) is 8 units, find the value of y. 8. Determine the ratio in which the point P ( a , -2 ) divi ...
... Find the are of the triangle formed by the points ( p + 1, 1 ) , ( 2p + 1 , 3 ) & ( 2p + 2 , 2p ) and show that these points are collinear if p = 2 or ½. 7. If the distance between the points (0,y) and (8,9) is 8 units, find the value of y. 8. Determine the ratio in which the point P ( a , -2 ) divi ...
Approximations of π
Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.Further progress was made only from the 15th century (Jamshīd al-Kāshī), and early modern mathematicians reached an accuracy of 35 digits by the 18th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in the years preceding 1873. Since the mid 20th century, approximation of π has been the task of electronic digital computers; the current record (as of May 2015) is at 13.3 trillion digits, calculated in October 2014.