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British Flag Theorem
In Euclidean geometry, the British flag theorem says that if a point ''P'' is chosen inside a rectangle ''ABCD'' then the sum of the squares of the Euclidean distances from ''P'' to two opposite corners of the rectangle equals the sum to the other two opposite corners. As an equation: : AP^2 + CP^2 = BP^2 + DP^2.\, The theorem also applies to points outside the rectangle, and more generally to the distances from a point in Euclidean space to the corners of a rectangle embedded into the space. Even more generally, if the sums of squares of distances from a point ''P'' to the two pairs of opposite corners of a parallelogram are compared, the two sums will not in general be equal, but the difference of the two sums will depend only on the shape of the parallelogram and not on the choice of ''P''.. The theorem can also be thought of as a generalisation of the Pythagorean theorem. Placing the point ''P'' on any of the four vertices of the rectangle yields the square of the diagonal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
British Flag Theorem Squares
British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies. ** Britishness, the British identity and common culture * British English, the English language as spoken and written in the United Kingdom or, more broadly, throughout the British Isles * Celtic Britons, an ancient ethno-linguistic group * Brittonic languages, a branch of the Insular Celtic language family (formerly called British) ** Common Brittonic, an ancient language Other uses *''Brit(ish)'', a 2018 memoir by Afua Hirsch *People or things associated with: ** Great Britain, an island ** United Kingdom, a sovereign state ** Kingdom of Great Britain (1707–1800) ** United Kingdom of Great Britain and Ireland (1801–1922) See also * Terminology of the British Isles * Alternative names for the British * English (other) * Britannic (other) * British Isles * Brit (other) * Briton (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
British Flag Theorem Proof3
British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies. ** Britishness, the British identity and common culture * British English, the English language as spoken and written in the United Kingdom or, more broadly, throughout the British Isles * Celtic Britons, an ancient ethno-linguistic group * Brittonic languages, a branch of the Insular Celtic language family (formerly called British) ** Common Brittonic, an ancient language Other uses *''Brit(ish)'', a 2018 memoir by Afua Hirsch *People or things associated with: ** Great Britain, an island ** United Kingdom, a sovereign state ** Kingdom of Great Britain (1707–1800) ** United Kingdom of Great Britain and Ireland (1801–1922) See also * Terminology of the British Isles * Alternative names for the British * English (other) * Britannic (other) * British Isles * Brit (other) * Briton (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dana S
Dana may refer to: People Given name * Dana (given name) Surname * Dana (surname) * Dana family of Cambridge, Massachusetts ** James Dwight Dana (1813–1895), scientist, zoological author abbreviation Dana Nickname or stage name * Dana International, stage name of singer Sharon Cohen * Dana Shum, the Shaw Brothers Hong Kong actress from 1973 to 1979 * Dana, stage name of Dana Rosemary Scallon (born 1951), Irish singer and former politician * Dana (South Korean singer) (born 1986), South Korean pop singer Places Ancient world * Ancient Dana or Tyana in Cappadocia, capital of a Neo-Hittite kingdom in the 1st millennium BC * Ancient Dana possibly associated with Tynna in Cappadocia Canada * CFS Dana, a former military radar installation in Saskatchewan, Canada * Dana Lake, a lake in Eeyou Istchee Baie-James, Quebec, Canada Ethiopia * Dana, Ethiopia, a village Iran * Dana County, an administrative subdivision of Iran * Dana Rural District, an administrative s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also a leading authority on Lewis Carroll. '' The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pizza Theorem
In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because it mimics a traditional pizza slicing technique. It shows that if two people share a pizza sliced into 8 pieces (or any multiple of 4 greater than 8), and take alternating slices, then they will each get an equal amount of pizza, irrespective of the central cutting point. Statement Let ''p'' be an interior point of the disk, and let ''n'' be a multiple of 4 that is greater than or equal to 8. Form ''n'' sectors of the disk with equal angles by choosing an arbitrary line through ''p'', rotating the line times by an angle of radians, and slicing the disk on each of the resulting lines. Number the sectors consecutively in a clockwise or anti-clockwise fashion. Then the pizza theorem states that: :'' The sum of the areas of the odd-numbered sectors equals the sum of the areas of the even-numbered sectors'' . History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Union Flag
The Union Jack, or Union Flag, is the ''de facto'' national flag of the United Kingdom. Although no law has been passed making the Union Flag the official national flag of the United Kingdom, it has effectively become such through precedent. It is sometimes asserted that the term ''Union Jack'' properly refers only to naval usage, but this assertion was dismissed by the Flag Institute in 2013 following historical investigations. The flag has official status in Canada, by parliamentary resolution, where it is known as the Royal Union Flag. It is the national flag of all British overseas territories, being localities within the British state, or realm, although local flags have also been authorised for most, usually comprising the blue or red ensign with the Union Flag in the canton and defaced with the distinguishing arms of the territory. These may be flown in place of, or along with (but taking precedence after) the national flag. Governors of British Overseas Territories ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Segment
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using a line above the symbols for the two endpoints (such as \overline). Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or a diagonal. When the end points both lie on a curve (such as a circle), a line segment is called a chord (of that curve). In real or complex vector spaces If ''V'' is a vector space o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flag Of The United Kingdom
The national flag of the United Kingdom is the Union Jack, also known as the Union Flag. The design of the Union Jack dates back to the Act of Union 1801 which united the Kingdom of Great Britain and the Kingdom of Ireland (previously in personal union) to create the United Kingdom of Great Britain and Ireland. The flag consists of the red cross of Saint George (patron saint of England (which also represents Wales)), edged in white, superimposed on the saltire of St Patrick (patron saint of Ireland), also edged in white, which are superimposed on the saltire of Saint Andrew (patron saint of Scotland). Wales is not represented in the Union Flag by Wales's patron saint, Saint David, because the flag was designed whilst Wales was part of the Kingdom of England. The flag proportions on land and the war flag used by the British Army have the proportions 3:5. The flag's height-to-length proportions at sea are 1:2. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Triangle
A right triangle (American English) or right-angled triangle ( British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right angle (that is, a 90- degree angle), i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry. The side opposite to the right angle is called the '' hypotenuse'' (side ''c'' in the figure). The sides adjacent to the right angle are called ''legs'' (or ''catheti'', singular: '' cathetus''). Side ''a'' may be identified as the side ''adjacent to angle B'' and ''opposed to'' (or ''opposite'') ''angle A'', while side ''b'' is the side ''adjacent to angle A'' and ''opposed to angle B''. If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a '' Pyt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthodiagonal Quadrilateral
In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. In other words, it is a four-sided figure in which the line segments between non-adjacent vertices are orthogonal (perpendicular) to each other. Special cases A kite is an orthodiagonal quadrilateral in which one diagonal is a line of symmetry. The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals. A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the ''n'' = 4 case of the bigg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perpendicular Line
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can be defined between two lines (or two line segments), between a line and a plane, and between two planes. Perpendicularity is one particular instance of the more general mathematical concept of ''orthogonality''; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as that between a surface and its ''normal vector''. Definitions A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides ''a'', ''b'' and the hypotenuse ''c'', often called the Pythagorean equation: :a^2 + b^2 = c^2 , The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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