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A. Harry Wheeler
Albert Harry Wheeler (18 January 1873, Leominster, Massachusetts – 1950) was an American mathematician, inventor, and mathematics teacher, known for physical construction (usually in paper) of polyhedral models and teaching this art to students. Education and career A. Harry Wheeler received in 1894 his Bachelor of Science degree from Worcester Polytechnic Institute. He taught high school in Worcester, Massachusetts from 1894 to 1896 and then was a graduate student in mathematics from 1896 to 1899 at Clark University, but left without a degree. He taught high school mathematics in Worcester from 1899 to 1920. His textbooks are ''First Course in Algebra'' (1907) and ''Examples in Algebra'' (1914). At age 47, returned in 1920 to graduate study in mathematics at Clark University, receiving a master's degree in 1921. Wheeler was an Invited Speaker of the ICM in 1924 at Toronto.Wheeler, Albert Harry (1924"Certain forms of the icosahedron and a method for deriving and designatin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leominster, Massachusetts
Leominster ( ) is a city in Worcester County, Massachusetts, United States. It is the second-largest city in Worcester County, with a population of 43,782 at the 2020 census. Leominster is located north of Worcester and northwest of Boston. Both Route 2 and Route 12 pass through Leominster. Interstate 190, Route 13, and Route 117 all have starting/ending points in Leominster. Leominster is bounded by Fitchburg and Lunenburg to the north, Lancaster to the east, Sterling and Princeton to the south, and Westminster to the west. History The region was originally inhabited by various divisions of the Pennacook or Nipmuc Native Americans, who lived along the Nashua River. The river provided fertile soil for the cultivation of corn, beans, squash and tobacco. European settlers began arriving in the mid-17th century and in 1653, the area of Leominster - which takes it name from the Herefordshire town of Leominster in England, was first founded as part of the town of Lanca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stellation
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until they meet each other again to form the closed boundary of a new figure. The new figure is a stellation of the original. The word ''stellation'' comes from the Latin ''stellātus'', "starred", which in turn comes from Latin ''stella'', "star". Stellation is the reciprocal or dual process to ''faceting''. Kepler's definition In 1619 Kepler defined stellation for polygons and polyhedra as the process of extending edges or faces until they meet to form a new polygon or polyhedron. He stellated the regular dodecahedron to obtain two regular star polyhedra, the small stellated dodecahedron and great stellated dodecahedron. He also stellated the regular octahedron to o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century American Mathematicians
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometers
A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * Manava (c. 750 BC–690 BC) – Euclidean geometry * Thales, Thales of Miletus (c. 624 BC – c. 546 BC) – Euclidean geometry * Pythagoras (c. 570 BC – c. 495 BC) – Euclidean geometry, Pythagorean theorem * Zeno of Elea (c. 490 BC – c. 430 BC) – Euclidean geometry * Hippocrates of Chios (born c. 470 – 410 BC) – first systematically organized ''Euclid's Elements, Stoicheia – Elements'' (geometry textbook) * Mozi (c. 468 BC – c. 391 BC) * Plato (427–347 BC) * Theaetetus (mathematician), Theaetetus (c. 417 BC – 369 BC) * Autolycus of Pitane (360–c. 290 BC) – astronomy, spherical geometry * Euclid (fl. 300 BC) – ''Euclid's Elements, Elements'', Euclidean geometry (sometimes called the "father of geometry") * Apolloni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Educators
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1950 Deaths
Year 195 ( CXCV) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Scrapula and Clemens (or, less frequently, year 948 ''Ab urbe condita''). The denomination 195 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Septimius Severus has the Roman Senate deify the previous emperor Commodus, in an attempt to gain favor with the family of Marcus Aurelius. * King Vologases V and other eastern princes support the claims of Pescennius Niger. The Roman province of Mesopotamia rises in revolt with Parthian support. Severus marches to Mesopotamia to battle the Parthians. * The Roman province of Syria is divided and the role of Antioch is diminished. The Romans annexed the Syrian cities of Edessa and Nisibis. Severus re-establish his he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1873 Births
Events January–March * January 1 ** Japan adopts the Gregorian calendar. ** The California Penal Code goes into effect. * January 17 – American Indian Wars: Modoc War: First Battle of the Stronghold – Modoc Indians defeat the United States Army. * February 11 – The Spanish Cortes deposes King Amadeus I, and proclaims the First Spanish Republic. * February 12 ** Emilio Castelar, the former foreign minister, becomes prime minister of the new Spanish Republic. ** The Coinage Act of 1873 in the United States is signed into law by President Ulysses S. Grant; coming into effect on April 1, it ends bimetallism in the U.S., and places the country on the gold standard. * February 20 ** The University of California opens its first medical school in San Francisco. ** British naval officer John Moresby discovers the site of Port Moresby, and claims the land for Britain. * March 3 – Censorship: The United States Congress enacts the Comstock Law, making it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge, Massachusetts
Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston, Worcester, and Springfield. It is one of two de jure county seats of Middlesex County, although the county's executive government was abolished in 1997. Situated directly north of Boston, across the Charles River, it was named in honor of the University of Cambridge in England, once also an important center of the Puritan theology embraced by the town's founders. Harvard University, the Massachusetts Institute of Technology (MIT), Lesley University, and Hult International Business School are in Cambridge, as was Radcliffe College before it merged with Harvard. Kendall Square in Cambridge has been called "the most innovative square mile on the planet" owing to the high concentration of successful startups that have emerged in the vicinity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non- stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles. Regular icosahedra There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Both have icosahedral symmetry. The term "regular icosahedron" generally refers to the convex variety, while the nonconvex form is called a ''great icosahedron''. Convex regular icosahedron The convex regular icosahedron is usually referred to simply as the ''regular icosahedron'', one of the five regular Platonic solids, and is represented by its Schläfli symbol , con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Brückner
Johannes Max Brückner (5 August 1860 – 1 November 1934) was a German geometer, known for his collection of polyhedral models. Education and career Brückner was born in Hartau, in the Kingdom of Saxony, a town that is now part of Zittau, Germany. He completed a Ph.D. at Leipzig University in 1886, supervised by Felix Klein and Wilhelm Scheibner, with a dissertation concerning conformal maps. After teaching at a grammar school in Zwickau, he moved to the gymnasium in Bautzen. Brückner is known for making many geometric models, particularly of stellated and uniform polyhedra, which he documented in his book ''Vielecke und Vielflache: Theorie und Geschichte'' (''Polygons and polyhedra: Theory and History'', Leipzig: B. G. Teubner, 1900). The shapes first studied in this book include the final stellation of the icosahedron and the compound of three octahedra, made famous by M. C. Escher's print ''Stars''. Joseph Malkevitch lists the publication of this book, which documen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron Model
A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material. Since there are 75 uniform polyhedra, including the five regular convex polyhedra, five polyhedral compounds, four Kepler-Poinsot polyhedra, and thirteen Archimedean solids, constructing or collecting polyhedron models has become a common mathematical recreation. Polyhedron models are found in mathematics classrooms much as globes in geography classrooms. Polyhedron models are notable as three-dimensional proof-of-concepts of geometric theories. Some polyhedra also make great centerpieces, tree toppers, Holiday decorations, or symbols. The Merkaba religious symbol, for example, is a stellated octahedron. Constructing large models offer challenges in engineering structural design. Construction Construction begins by choosing a ''size'' of the model, either the ''length'' of its edges or the ''heigh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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