Quaternions are turning tomb raiders on their heads
... by another quaternion t of unit norm. What is the composite transformation? Well, the composite takes q ∈ H− to tuqu∗ t∗ = (tu)q(tu)∗ . This shows the composite of the two rotations is another rotation, in fact the rotation corresponding to the unit norm quaternion tu. Quaternions and their Generali ...
... by another quaternion t of unit norm. What is the composite transformation? Well, the composite takes q ∈ H− to tuqu∗ t∗ = (tu)q(tu)∗ . This shows the composite of the two rotations is another rotation, in fact the rotation corresponding to the unit norm quaternion tu. Quaternions and their Generali ...
The Number of Primes: Limitless
... also the only even prime number. Why? Every even number is divisible by itself and 1 but every even number is also divisible by 2. Therefore, every even number has more factors other than itself and 1. What makes prime numbers special is that they form the “building blocks” of every other number. Th ...
... also the only even prime number. Why? Every even number is divisible by itself and 1 but every even number is also divisible by 2. Therefore, every even number has more factors other than itself and 1. What makes prime numbers special is that they form the “building blocks” of every other number. Th ...
Estimating With Square Roots
... Estimating Square Roots Worksheet – Homework 1. What are the two whole numbers closest to ...
... Estimating Square Roots Worksheet – Homework 1. What are the two whole numbers closest to ...
Slide 1
... What is counting? • Working on an one-one correspondence between a basket of fruits and the Natural Number. • By the time we empty the basket, the count (number) of fruits in the basket in that Natural Number we arrive at. • What if sometimes we cannot stop? ...
... What is counting? • Working on an one-one correspondence between a basket of fruits and the Natural Number. • By the time we empty the basket, the count (number) of fruits in the basket in that Natural Number we arrive at. • What if sometimes we cannot stop? ...
Document
... finite fields, the real numbers, and the complex numbers. In 1985, after mathematicians had been working on Fermat’s Last Theorem for about 350 years, Gerhard Frey suggested that if we assumed Fermat’s Last Theorem was false, the existence of an elliptic curve y 2 x( x a n )( x bn ) where a, b ...
... finite fields, the real numbers, and the complex numbers. In 1985, after mathematicians had been working on Fermat’s Last Theorem for about 350 years, Gerhard Frey suggested that if we assumed Fermat’s Last Theorem was false, the existence of an elliptic curve y 2 x( x a n )( x bn ) where a, b ...
Whole Numbers and Decimals
... The Moral of the Story • To order positive and negative numbers, use their position on the number line to assess their relative value. ...
... The Moral of the Story • To order positive and negative numbers, use their position on the number line to assess their relative value. ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.