Floor and ceiling functionsIn mathematics and computer science, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). For example (floor), ⌊2.4⌋ = 2, ⌊−2.4⌋ = −3, and for ceiling; ⌈2.4⌉ = 3, and ⌈−2.4⌉ = −2. Historically, the floor of x has been–and still is–called the integral part or integer part of x, often denoted [x] (as well as a variety of other notations).
Complex conjugateIn mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if and are real numbers then the complex conjugate of is The complex conjugate of is often denoted as or . In polar form, if and are real numbers then the conjugate of is This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: (or in polar coordinates).
Architecture of the medieval cathedrals of EnglandThe medieval cathedrals of England, which date from between approximately 1040 and 1540, are a group of twenty-six buildings that constitute a major aspect of the country's artistic heritage and are among the most significant material symbols of Christianity. Though diverse in style, they are united by a common function. As cathedrals, each of these buildings serves as central church for an administrative region (or diocese) and houses the throne of a bishop (Late Latin ecclēsia cathedrālis, from the Greek, καθέδρα).
