|
Indiana Pi Bill
The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative fiat. Despite its name, the main result claimed by the bill is a method to square the circle, although it does imply various incorrect values of the mathematical constant , the ratio of the circumference of a circle to its diameter. The bill, written by a physician who was an amateur mathematician, never became law due to the intervention of Prof. C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote. The mathematical impossibility of squaring the circle using only compass and straightedge constructions, suspected since ancient times, had been rigorously proven 15 years previously, in 1882 by Ferdinand von Lindemann. Better approximations of than those implied by the bill have been known since ancient times. Legislative history ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indiana General Assembly
The Indiana General Assembly is the state legislature, or legislative branch, of the state of Indiana. It is a bicameral legislature that consists of a lower house, the Indiana House of Representatives, and an upper house, the Indiana Senate. The General Assembly meets annually at the Indiana Statehouse in Indianapolis. Members of the General Assembly are elected from districts that are realigned every ten years. Representatives serve terms of two years and senators serve terms of four years. Both houses can create bills, but bills must pass both houses before it can be submitted to the governor and enacted into law. Currently, the Republican Party holds supermajorities in both chambers of the General Assembly. Republicans outnumber Democrats in the Senate by a 40-10 margin, and in the House of Representatives by a 70-30 margin. Structure The Indiana General Assembly is made up of two houses, the House of Representatives and the Senate. Indiana has a part-time legislature ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squaring The Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (\pi) is a transcendental number. That is, \pi is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if \pi were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been found. Despite the proof that it is impossible, attempts to square the circle have been common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides. It is the only regular polygon whose internal angle, central angle, and external angle are all equal (90°), and whose diagonals are all equal in length. A square with vertices ''ABCD'' would be denoted . Characterizations A convex quadrilateral is a square if and only if it is any one of the following: * A rectangle with two adjacent equal sides * A rhombus with a right vertex angle * A rhombus with all angles equal * A parallelogram with one right vertex angle and two adjacent equal sides * A quadrilateral with four equal sides and four right angles * A quadrilateral where the diagonals are equal, and are the perpendicular bisectors of each other (i.e., a rhombus with equal diagonals) * A convex quadrilateral with successiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral Polygon
In geometry, an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, an equilateral polygon does not need to also be equiangular (have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon does not need to be a convex polygon: it could be concave or even self-intersecting. Examples All regular polygons and edge-transitive polygons are equilateral. When an equilateral polygon is non-crossing and cyclic (its vertices are on a circle) it must be regular. An equilateral quadrilateral must be convex; this polygon is a rhombus (possibly a square). A convex equilateral pentagon can be described by two consecutive angles, which together determine the other angles. However, equilateral pentagons, and equilateral polygons with more than five sides, can also be concave, and if concave pentagons are allowed then two angles are no longer sufficient to determine the sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compass And Straightedge
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really means: see Markable rulers below.) More formally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes
Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time,* * * * * * * * * * Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Heath, Thomas L. 1897. ''Works of Archimedes''. Archimedes' other mathematical achievements include deriving an approximation of pi, defining and in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because . Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'', which is denoted by \sqrt, where the symbol \sqrt is called the ''radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case 9. For nonnegative , the principal square root can also be written in exponent notation, as . Every positive number has two square roots: \sqrt, which is positive, and -\sqrt, which is negative. The two roots can be written more concisely using the ± sign as \plusmn\sqrt. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chicago Tribune
The ''Chicago Tribune'' is a daily newspaper based in Chicago, Illinois, United States, owned by Tribune Publishing. Founded in 1847, and formerly self-styled as the "World's Greatest Newspaper" (a slogan for which WGN radio and television are named), it remains the most-read daily newspaper in the Chicago metropolitan area and the Great Lakes region. It had the sixth-highest circulation for American newspapers in 2017. In the 1850s, under Joseph Medill, the ''Chicago Tribune'' became closely associated with the Illinois politician Abraham Lincoln, and the Republican Party's progressive wing. In the 20th century under Medill's grandson, Robert R. McCormick, it achieved a reputation as a crusading paper with a decidedly more American-conservative anti-New Deal outlook, and its writing reached other markets through family and corporate relationships at the ''New York Daily News'' and the ''Washington Times-Herald.'' The 1960s saw its corporate parent owner, Tribune Company, rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Postpone Indefinitely
In parliamentary procedure, the motion to postpone indefinitely is a subsidiary motion used to kill a main motion without taking a direct vote on it. This motion does not actually "postpone" it. Explanation and use In ''Robert's Rules of Order Newly Revised'' (RONR), the effect of the motion, if adopted, is not to "postpone" the main motion, but rather to prevent action on it for the duration of the current session. It can be used when the assembly does not wish to adopt a motion, but explicitly rejecting it would perhaps be embarrassing, such as a motion to endorse a candidate for a political office. The motion to postpone indefinitely is the lowest-ranking of all motions other than the main motion, and therefore it cannot be made while any other subsidiary, privileged or incidental motion is pending. Because debate on the motion to postpone indefinitely may go into the merits of the pending main motion, it may provide members of the assembly with additional opportunities to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indiana Academy Of Science
Indiana () is a U.S. state in the Midwestern United States. It is the 38th-largest by area and the 17th-most populous of the 50 States. Its capital and largest city is Indianapolis. Indiana was admitted to the United States as the 19th state on December 11, 1816. It is bordered by Lake Michigan to the northwest, Michigan to the north, Ohio to the east, the Ohio River and Kentucky to the south and southeast, and the Wabash River and Illinois to the west. Various indigenous peoples inhabited what would become Indiana for thousands of years, some of whom the U.S. government expelled between 1800 and 1836. Indiana received its name because the state was largely possessed by native tribes even after it was granted statehood. Since then, settlement patterns in Indiana have reflected regional cultural segmentation present in the Eastern United States; the state's northernmost tier was settled primarily by people from New England and New York, Central Indiana by migrants from t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indianapolis
Indianapolis (), colloquially known as Indy, is the state capital and most populous city of the U.S. state of Indiana and the seat of Marion County. According to the U.S. Census Bureau, the consolidated population of Indianapolis and Marion County was 977,203 in 2020. The "balance" population, which excludes semi-autonomous municipalities in Marion County, was 887,642. It is the 15th most populous city in the U.S., the third-most populous city in the Midwest, after Chicago and Columbus, Ohio, and the fourth-most populous state capital after Phoenix, Arizona, Austin, Texas, and Columbus. The Indianapolis metropolitan area is the 33rd most populous metropolitan statistical area in the U.S., with 2,111,040 residents. Its combined statistical area ranks 28th, with a population of 2,431,361. Indianapolis covers , making it the 18th largest city by land area in the U.S. Indigenous peoples inhabited the area dating to as early as 10,000 BC. In 1818, the Lenape relinquished their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Language
German ( ) is a West Germanic languages, West Germanic language mainly spoken in Central Europe. It is the most widely spoken and Official language, official or co-official language in Germany, Austria, Switzerland, Liechtenstein, and the Italy, Italian province of South Tyrol. It is also a co-official language of Luxembourg and German-speaking Community of Belgium, Belgium, as well as a national language in Namibia. Outside Germany, it is also spoken by German communities in France (Bas-Rhin), Czech Republic (North Bohemia), Poland (Upper Silesia), Slovakia (Bratislava Region), and Hungary (Sopron). German is most similar to other languages within the West Germanic language branch, including Afrikaans, Dutch language, Dutch, English language, English, the Frisian languages, Low German, Luxembourgish, Scots language, Scots, and Yiddish. It also contains close similarities in vocabulary to some languages in the North Germanic languages, North Germanic group, such as Danish lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_by_Thomas_Degeorge.png "Click for more on -> Archimedes")
