Artemis and PythagorasThe daughter of Leto and Zeus, and the twin of Apollo. Artemis is the goddess of the wilderness, the hunt and wild animals, and fertility (she became a goddess of fertility and childbirth mainly in cities). She was often depicted with the crescent of the moon above her forehead and was sometimes identified with Selene (goddess of the moon). Artemis was one of the Olympians and a virgin goddess. Her main vocation was to roam mountain forests and uncultivated land with her nymphs in attendance hunting for lions, panthers, hinds and stags. Contradictory to the later, she helped in protecting and seeing to their well-being, also their safety and reproduction. She was armed with a bow and arrows which were made by Hephaestus and the Cyclopes.
In one legend, Artemis was born one day before her brother Apollo. Her mother gave birth to her on the island of Ortygia, then, almost immediately after her birth, she helped her mother to cross the straits over to Delos, where she then delivered Apollo. This was the beginning of her role as guardian of young children and patron of women in childbirth. Being a goddess of contradictions, she was the protectress of women in labor, but it was said that the arrows of Artemis brought them sudden death while giving birth. As was her brother, Apollo, Artemis was a divinity of healing, but also brought and spread diseases such as leprosy, rabies and even gout.
Being associated with chastity, Artemis at an early age (in one legend she was three years old) asked her father, the great god Zeus, to grant her eternal virginity. Also, all her companions were virgins. Artemis was very protective of her purity, and gave grave punishment to any man who attempted to dishonor her in any form. Actaeon, while out hunting, accidentally came upon Artemis and her nymphs, who bathing naked in a secluded pool. Seeing them in all their naked beauty, the stunned Actaeon stopped and gazed at them, but when Artemis saw him ogling them, she transformed him into a stag. Then, incensed with disgust, she set his own hounds upon him. They chased and killed what they thought was another stag, but it was their master. As with Orion, a giant and a great hunter, there are several legends which tell of his death, one involving Artemis. It is said that he tried to rape the virgin goddess, so killed him with her bow and arrows. Another says she conjured up a scorpion which killed Orion and his dog. Orion became a constellation in the night sky, and his dog became Sirius, the dog star. Yet another version says it was the scorpion which stung him and was transformed into the constellation with Orion, the later being Scorpio. Artemis was enraged when one of her nymphs, Callisto, allowed Zeus to seduce her, but the great god approached her in one of his guises; he came in the form of Artemis. The young nymph was unwittingly tricked, and she gave birth to Arcas, the ancestor of the Arcadians, but Artemis showed no mercy and changed her into a bear. She then shot and killed her. As Orion, she was sent up to the heavens, and became the constellation of the Great Bear (which is also known as the Plough).
Artemis was very possessive. She would show her wrath on anyone who disobeyed her wishes, especially against her sacred animals. Even the great hero Agamemnon came upon the wrath of Artemis, when he killed a stag in her sacred grove. His punishment came when his ships were becalmed, while he made his way to besiege Troy. With no winds to sail his ships he was told by the seer Calchas that the only way Artemis would bring back the winds was for him to sacrifice his daughter Iphigenia. Some versions say he did sacrifice Iphigenia, others that Artemis exchanged a deer in her place, and took Iphigenia to the land of the Tauri (the Crimea) as a priestess, to prepare strangers for sacrifice to Artemis.
Artemis with her twin brother, Apollo, put to death the children of Niobe. The reason being that Niobe, a mere mortal, had boasted to Leto, the mother of the divine twins, that she had bore more children, which must make her superior to Leto. Apollo being outraged at such an insult on his mother, informed Artemis. The twin gods hunted them down and shot them with their bows and arrows; Apollo killed the male children and Artemis the girls.
Artemis was worshiped in most Greek cities but only as a secondary deity. However, to the Greeks in Asia Minor (modern day Turkey) she was a prominent deity. In Ephesus, a principal city of Asia Minor, a great temple was built in her honor, which became one of the "Seven Wonders of the Ancient World". But at Ephesus she was worshiped mainly as a fertility goddess, and was identified with Cybele the mother goddess of eastern lands. The cult statues of the Ephesian Artemis differ greatly from those of mainland Greece, whereas she is depicted as a huntress with her bow and arrows. Those found at Ephesus show her in the eastern style, standing erect with numerous nodes on her chest. There have been many theories as to what they represent. Some say they are breasts, others that they are bulls testes which were sacrificed to her. Which is the true interpretation remains uncertain, but each represent fertility.
There were festivals in honor of Artemis, such as the Brauronia, which was held in Brauron; and the festival of Artemis Orthia, held at Sparta, when young Spartan boys would try to steal cheeses from the altar. As they tried they would be whipped, the meaning of Orthia and the nature of the ritual whipping has been lost and there is no logical explanation or translation. Among the epithets given to Artemis are: Potnia Theron (mistress of wild animals) this title was mentioned by the great poet Homer; Kourotrophos (nurse of youth's); Locheia (helper in childbirth); Agrotera (huntress); and Cynthia (taken from her birthplace on Mount Cynthus on Delos). When young girls reached puberty they were initiated into her cult, but when they decided to marry, which Artemis was not against, they were asked to lay in front of the altar all the paraphernalia of their virginity, toys, dolls and locks of their hair, they then left the domain of the virgin goddess.
Pythagoras of Samos, c.560-c.480 BC, was a Greek philosopher and religious leader who was responsible for important developments in the history of mathematics, astronomy, and the theory of music. He migrated to Croton and founded a philosophical and religious school there that attracted many followers. Because no reliable contemporary records survive, and because the school practiced both secrecy and communalism, the contributions of Pythagoras himself and those of his followers cannot be distinguished. Pythagoreans believed that all relations could be reduced to number relations ("all things are numbers"). This generalization stemmed from certain observations in music, mathematics, and astronomy.
The Pythagoreans noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments. They knew, as did the Egyptians before them, that any triangle whose sides were in the ratio 3:4:5 was a right-angled triangle. The so-called Pythagorean theorem, that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, may have been known in Babylonia, where Pythagoras traveled in his youth; the Pythagoreans, however, are usually credited with the first proof of this theorem.
In astronomy, the Pythagoreans were well aware of the periodic numerical relations of heavenly bodies. The CELESTIAL SPHERES of the planets were thought to produce a harmony called the music of the spheres. Pythagoreans believed that the earth itself was in motion. The most important discovery of this school--which upset Greek mathematics, as well as the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties--was the incommensurability of the diagonal of a square with its side. This result showed the existence of IRRATIONAL NUMBERS.
Whereas much of the Pythagorean doctrine that has survived consists of numerology and number mysticism, the influence of the idea that the world can be understood through mathematics was extremely important to the development of science and mathematics.
In one legend, Artemis was born one day before her brother Apollo. Her mother gave birth to her on the island of Ortygia, then, almost immediately after her birth, she helped her mother to cross the straits over to Delos, where she then delivered Apollo. This was the beginning of her role as guardian of young children and patron of women in childbirth. Being a goddess of contradictions, she was the protectress of women in labor, but it was said that the arrows of Artemis brought them sudden death while giving birth. As was her brother, Apollo, Artemis was a divinity of healing, but also brought and spread diseases such as leprosy, rabies and even gout.
Being associated with chastity, Artemis at an early age (in one legend she was three years old) asked her father, the great god Zeus, to grant her eternal virginity. Also, all her companions were virgins. Artemis was very protective of her purity, and gave grave punishment to any man who attempted to dishonor her in any form. Actaeon, while out hunting, accidentally came upon Artemis and her nymphs, who bathing naked in a secluded pool. Seeing them in all their naked beauty, the stunned Actaeon stopped and gazed at them, but when Artemis saw him ogling them, she transformed him into a stag. Then, incensed with disgust, she set his own hounds upon him. They chased and killed what they thought was another stag, but it was their master. As with Orion, a giant and a great hunter, there are several legends which tell of his death, one involving Artemis. It is said that he tried to rape the virgin goddess, so killed him with her bow and arrows. Another says she conjured up a scorpion which killed Orion and his dog. Orion became a constellation in the night sky, and his dog became Sirius, the dog star. Yet another version says it was the scorpion which stung him and was transformed into the constellation with Orion, the later being Scorpio. Artemis was enraged when one of her nymphs, Callisto, allowed Zeus to seduce her, but the great god approached her in one of his guises; he came in the form of Artemis. The young nymph was unwittingly tricked, and she gave birth to Arcas, the ancestor of the Arcadians, but Artemis showed no mercy and changed her into a bear. She then shot and killed her. As Orion, she was sent up to the heavens, and became the constellation of the Great Bear (which is also known as the Plough).
Artemis was very possessive. She would show her wrath on anyone who disobeyed her wishes, especially against her sacred animals. Even the great hero Agamemnon came upon the wrath of Artemis, when he killed a stag in her sacred grove. His punishment came when his ships were becalmed, while he made his way to besiege Troy. With no winds to sail his ships he was told by the seer Calchas that the only way Artemis would bring back the winds was for him to sacrifice his daughter Iphigenia. Some versions say he did sacrifice Iphigenia, others that Artemis exchanged a deer in her place, and took Iphigenia to the land of the Tauri (the Crimea) as a priestess, to prepare strangers for sacrifice to Artemis.
Artemis with her twin brother, Apollo, put to death the children of Niobe. The reason being that Niobe, a mere mortal, had boasted to Leto, the mother of the divine twins, that she had bore more children, which must make her superior to Leto. Apollo being outraged at such an insult on his mother, informed Artemis. The twin gods hunted them down and shot them with their bows and arrows; Apollo killed the male children and Artemis the girls.
Artemis was worshiped in most Greek cities but only as a secondary deity. However, to the Greeks in Asia Minor (modern day Turkey) she was a prominent deity. In Ephesus, a principal city of Asia Minor, a great temple was built in her honor, which became one of the "Seven Wonders of the Ancient World". But at Ephesus she was worshiped mainly as a fertility goddess, and was identified with Cybele the mother goddess of eastern lands. The cult statues of the Ephesian Artemis differ greatly from those of mainland Greece, whereas she is depicted as a huntress with her bow and arrows. Those found at Ephesus show her in the eastern style, standing erect with numerous nodes on her chest. There have been many theories as to what they represent. Some say they are breasts, others that they are bulls testes which were sacrificed to her. Which is the true interpretation remains uncertain, but each represent fertility.
There were festivals in honor of Artemis, such as the Brauronia, which was held in Brauron; and the festival of Artemis Orthia, held at Sparta, when young Spartan boys would try to steal cheeses from the altar. As they tried they would be whipped, the meaning of Orthia and the nature of the ritual whipping has been lost and there is no logical explanation or translation. Among the epithets given to Artemis are: Potnia Theron (mistress of wild animals) this title was mentioned by the great poet Homer; Kourotrophos (nurse of youth's); Locheia (helper in childbirth); Agrotera (huntress); and Cynthia (taken from her birthplace on Mount Cynthus on Delos). When young girls reached puberty they were initiated into her cult, but when they decided to marry, which Artemis was not against, they were asked to lay in front of the altar all the paraphernalia of their virginity, toys, dolls and locks of their hair, they then left the domain of the virgin goddess.
Pythagoras of Samos, c.560-c.480 BC, was a Greek philosopher and religious leader who was responsible for important developments in the history of mathematics, astronomy, and the theory of music. He migrated to Croton and founded a philosophical and religious school there that attracted many followers. Because no reliable contemporary records survive, and because the school practiced both secrecy and communalism, the contributions of Pythagoras himself and those of his followers cannot be distinguished. Pythagoreans believed that all relations could be reduced to number relations ("all things are numbers"). This generalization stemmed from certain observations in music, mathematics, and astronomy.
The Pythagoreans noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments. They knew, as did the Egyptians before them, that any triangle whose sides were in the ratio 3:4:5 was a right-angled triangle. The so-called Pythagorean theorem, that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, may have been known in Babylonia, where Pythagoras traveled in his youth; the Pythagoreans, however, are usually credited with the first proof of this theorem.
In astronomy, the Pythagoreans were well aware of the periodic numerical relations of heavenly bodies. The CELESTIAL SPHERES of the planets were thought to produce a harmony called the music of the spheres. Pythagoreans believed that the earth itself was in motion. The most important discovery of this school--which upset Greek mathematics, as well as the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties--was the incommensurability of the diagonal of a square with its side. This result showed the existence of IRRATIONAL NUMBERS.
Whereas much of the Pythagorean doctrine that has survived consists of numerology and number mysticism, the influence of the idea that the world can be understood through mathematics was extremely important to the development of science and mathematics.