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In 1968 Shirley Chisholm became the first Black woman elected to the United States Congress. In 1972 she launched a campaign for the Democratic presidential nomination, breaking another political barrier.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
Hypsicles (Ancient Greek: Ὑψικλῆς, romanized: Hypsiklēs; c. 190 – c. 120 BCE) was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and possibly the Book XIV of Euclid's Elements. Hypsicles lived in Alexandria.[1]
Although little is known about the life of Hypsicles, it is believed that he authored the astronomical work On Ascensions. The mathematician Diophantus of Alexandria noted on a definition of polygonal numbers, due to Hypsicles:[2]
If there are as many numbers as we please beginning from 1 and increasing by the same common difference, then, when the common difference is 1, the sum of all the numbers is a triangular number; when 2 a square; when 3, a pentagonal number [and so on]. And the number of angles is called after the number which exceeds the common difference by 2, and the side after the number of terms including 1.
In On Ascensions (Ἀναφορικός and sometimes translated On Rising Times), Hypsicles proves a number of propositions on arithmetical progressions and uses the results to calculate approximate values for the times required for the signs of the zodiac to rise above the horizon.[3] It is thought that this is the work from which the division of the circle into 360 parts may have been adopted[4] since it divides the day into 360 parts, a division possibly suggested by Babylonian astronomy,[5] although this is mere speculation and no actual evidence is found to support this. Heath 1921 notes, "The earliest extant Greek book in which the division of the circle into 360 degrees appears".[6]
This work by Hypsicles is believed to represent the earliest extant Greek text to use the Babylonian division of the zodiac into 12 signs of 30 degrees each.[7]
Hypsicles is more famously known for possibly writing the Book XIV of Euclid's Elements. The book may have been composed on the basis of a treatise by Apollonius. The book continues Euclid's comparison of regular solids inscribed in spheres, with the chief result being that the ratio of the surfaces of the dodecahedron and icosahedron inscribed in the same sphere is the same as the ratio of their volumes, the ratio being .[4]
Heath further notes, "Hypsicles says also that Aristaeus, in a work entitled Comparison of the five figures, proved that the same circle circumscribes both the pentagon of the dodecahedron and the triangle of the icosahedron inscribed in the same sphere; whether this Aristaeus is the same as the Aristaeus of the Solid Loci, the elder (Aristaeus the Elder) contemporary of Euclid, we do not know."[6]
Hypsicles letter was a preface of the supplement taken from Euclid's Book XIV, part of the thirteen books of Euclid's Elements, featuring a treatise.[1]
Basilides of Tyre, O Protarchus, when he came to Alexandria and met my father, spent the greater part of his sojourn with him on account of the bond between them due to their common interest in mathematics. And on one occasion, when looking into the tract written by Apollonius (Apollonius of Perga) about the comparison of the dodecahedron and icosahedron inscribed in one and the same sphere, that is to say, on the question what ratio they bear to one another, they came to the conclusion that Apollonius' treatment of it in this book was not correct; accordingly, as I understood from my father, they proceeded to amend and rewrite it. But I myself afterwards came across another book published by Apollonius, containing a demonstration of the matter in question, and I was greatly attracted by his investigation of the problem. Now the book published by Apollonius is accessible to all; for it has a large circulation in a form which seems to have been the result of later careful elaboration. For my part, I determined to dedicate to you what I deem to be necessary by way of commentary, partly because you will be able, by reason of your proficiency in all mathematics and particularly in geometry, to pass an expert judgment upon what I am about to write, and partly because, on account of your intimacy with my father and your friendly feeling towards myself, you will lend a kindly ear to my disquisition. But it is time to have done with the preamble and to begin my treatise itself.
In ancient times it was not uncommon to attribute to a celebrated author works that were not by him; thus, some versions of Euclid's Elements include a fourteenth and even a fifteenth book, both shown by later scholars to be apocryphal. The so-called Book XIV continues Euclid's comparison of the regular solids inscribed in a sphere, the chief results being that the ratio of the surfaces of the dodecahedron and icosahedron inscribed in the same sphere is the same as the ratio of their volumes, the ratio being that of the edge of the cube to the edge of the icosahedron, that is, It is thought that this book may have been composed by Hypsicles on the basis of a treatise (now lost) by Apollonius comparing the dodecahedron and icosahedron. (Hypsicles, who probably lived in the second half of the second century B.C., is thought to be the author of an astronomical work, De ascensionibus, from which the division of the circle into 360 parts may have been adopted.)
It is possible that he took over from Hypsicles, who earlier had divided the day into 360 parts, a subdivision that may have been suggested by Babylonian astronomy
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
Hypsicles (Ancient Greek: Ὑψικλῆς, romanized: Hypsiklēs; c. 190 – c. 120 BCE) was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and possibly the Book XIV of Euclid's Elements. Hypsicles lived in Alexandria.
Basilides of Tyre (Ancient Greek: Βασιλείδης) was a mathematician, mentioned by Hypsicles in his prefatory letter of Euclid's Elements, Book XIV. Barnes and Brunschwig suggested that Basilides of Tyre and Basilides the Epicurean could be the same Basilides.
Alexandria is a major city in Egypt. Lying at the western edge of the Nile River Delta, it extends about 40 km (25 mi) along the country's northern coast. It is Egypt's principal seaport, the second largest city after Cairo, and the largest city on the Mediterranean coast. Founded in 331 BC by Alexander the Great, Alexandria was one of the largest and most important cities of antiquity and a leading hub for science, culture, and scholarship. Nicknamed the "Bride of the Mediterranean" and "Pearl of the Mediterranean Coast", the city is a popular tourist destination and a major industrial centre. It is the sixth-largest city in the Arab world, seventh-largest city in the Middle East, and the eleventh-largest city in Africa. The capital of the Alexandria Governorate, Alexandria is considered an industrial hub and is home to the Alexandria Shipyard. The city also has a large financial sector, and its ancient port Alexandria is one of the busiest ports in the country. Alexandria is the host city of the annual Alexandria Mediterranean Film Festival, held at the Bibliotheca Alexandrina. The city is also the home of the Alexandria Opera House, the Alexandria Museum of Fine Arts and the Alexandria National Museum. The city hosts many sporting events, and is the home of the association football club Al Ittihad. Alexandria extends beyond its administrative municipal city limits as well as its urban agglomeration, with a population of 6,100,000 in 2023 over an area of 1,661 square kilometres (641 sq mi). Alexandria was originally established near an ancient Egyptian settlement named Rhacotis, which later became its Egyptian quarter. The city was made the capital of the Ptolemaic Kingdom and became the foremost commercial, intellectual, and cultural centre for much of the Hellenistic age and late antiquity; at one time, it was the most populous city in the ancient world. Alexandria was best known for the Lighthouse of Alexandria (Pharos), one of the Seven Wonders of the Ancient World; its Great Library, the largest in the ancient world; and the Catacombs of Kom El Shoqafa, one of the Seven Wonders of the Middle Ages. Alexandria retained its status as one of the leading cities of the Mediterranean world for almost a millennium, serving as the Egyptian capital until a new capital was founded at Fustat, now part of Cairo. The city was a major hub of early Christianity and hosted the Patriarchate of Alexandria, one of the leading Christian centers in the Eastern Roman Empire; the modern Coptic Orthodox Church and the Greek Orthodox Church of Alexandria both lay claim to this ancient heritage. By the mid-seventh century, the city continued to serve as a trading hub and naval base. From the late 18th century, it was a major centre of the international shipping industry and one of the most important trading centers in the world, owing to the easy overland connection between the Mediterranean and Red Seas and the lucrative trade in Egyptian cotton. Alexandria's rebirth began in the early 19th century under Muhammad Ali, considered the founder of modern Egypt, who implemented infrastructure projects and modernisation efforts.
Euclid (; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. In addition to the Elements, Euclid wrote a central early text in the optics field, Optics, and lesser-known works including Data and Phaenomena. Euclid's authorship of On Divisions of Figures and Catoptrics has been questioned. He is thought to have written many lost works.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Mae Jemison, aboard Space Shuttle Endeavour in 1992.
