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# Eudoxus

due may 5 - presentation may 6

#### Transcript of Eudoxus

Eudoxus by becky grinberg Eudoxus was a famous mathmetician, astronomer, and philosopher from Cnidus (near present day Turkey). He was born c. 400 BC in Cnidus to his father Aischines. http://www.nndb.com/people/658/000096370/eudoxus-1.jpg http://www.mlahanas.de/Greeks/Cities/CnidusSat.jpg http://www.clker.com/ Travels Tarentum Studied here (present day Italy) with his teacher Archytas.

Together, they worked on the famous duplicating the cube problem.

Eudoxus solved it by using curved lines, with his "Kampyle of Eudoxus". http://www.hellenica.de/Griechenland/Mythos/Bild/Archytas.jpg Archytas doubling the cube http://www.karlin.mff.cuni.cz/~rokyta/api/obrazky/dblcube.gif http://www-history.mcs.st-and.ac.uk/Curvepics/Kampyle/Kampyle1.gif a^2x^4=b^4(x^2+y^2) Athens Eudoxus visited Athens for 2 months.

While here, he attended Plato's philosophy lectures.

He was very poor while he lived in Athens, and just to get to the lectures Eudoxus had to walk 11 miles back and forth daily.Thomes Little Heath describes Eudoxus as "... so poor was he that he took up his abode at the Piraeus and trudged to Athens and back on foot each day." in his novel. Egypt Studied here with priests at Heliopolis. This is where Eudoxus became interested in astronomy, making many observations from an observatory between Heliopolis and Cercesura. http://www.iho-ohi.org/wp-content/athens-greece.jpg http://farm3.static.flickr.com/2706/4341988410_0eca737378_o.jpg http://www.mynews.in/News/dailyimage/news/astronomy--med--1.jpg http://clipart.peirceinternet.com/png/telescope1.png Cyzicus Cyzicus was an ancient town of Mysia in Asia Minor.

Eudoxus visited here, starting school. Supposedly, among his students was the famous Aristotle.

He gathered many students of his own during his travels. The success of his teaching may have been a cause of his and Plato's falling out. http://www.mlahanas.de/Greeks/Cities/MinorAsiaCities.gif Return to Cnidus http://www.freefunfiles.com/images/ourfreefunfiles/screensavers/outer-space-vol1.jpg Contributions Mathematics Astronomy Theory of Proportion Comparing possibly irrational lengths without ratios. This helped define the meaning of the equality between two ratios. If a:b and c:d where a, b, c, or d are possibly irrational: i. ma < nb, then mc < nd

ii. ma = nb, then mc = nd

iii. ma > nb, then mc > nd Method of Exhaustion Calculating an area by approximating it by the areas of a sequence of polygons. ex. filling up the interior of a circle by inscribing a polygon with more and more sides. wikipedia.org Eudoxus found that planetary motion could be explained using different axis rotations on a globe. http://www.beyondpluto.net/LYCIA/EudoxanMoon.jpg Each axis revolves around a different rotation of the planet. These represent different periods of time of a rotation: for example one axis represents a 24 hour cycle, or the cycle we know as a day.

http://www-groups.dcs.st-and.ac.uk/~history/Diagrams/Eudoxus.gif The Moon's Spheres 2nd ring is a monthly rotation of the moon's motion through the zodiac. 3rd ring is also a monthly rotation, but slightly angled. This explains motion in latitude. The 5 Visible Planets Venus, Mercury, Mars, Saturn, Jupiter Outermost ring is daily motion, 24 hours. 2nd is the planet's motion through the zodiac. The 3rd and 4th rings trace out a figure 8 hippopede due to retrograde - when a planet seems to slow down before it continues in the zodiac. This idea was later expanded by the mathmetician Archimedes. This was included in Euclid "Elements" Vol. 5. Credit http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Eudoxus.html http://en.wikipedia.org/wiki/Eudoxus_of_Cnidus http://www.math.tamu.edu/~dallen/history/eudoxus/eudoxus.html http://www2.stetson.edu/~efriedma/periodictable/html/Xe.html http://www.mlahanas.de/Greeks/Eudoxus.htm http://scienceworld.wolfram.com/biography/Eudoxus.html http://www.salzgeber.at/astro/moon/aristoteles_Eudoxus.jpg http://www.orbiterwiki.org/images/9/94/MoonThumbTransparent.png http://upload.wikimedia.org/wikipedia/commons/e/e1/Jupiter_(transparent).png Outermost sphere rotates westward every 24 hours:

rising and setting. Eudoxus returned back to Cnidus after his many travels. When he returned, the rulers had been overthrown & democracy established. With no rulers, the citizens asked Eudoxus to write them a constitution. He wrote it & ended up serving on his city's assembly.

He built an observatory and continued his studied until his death in c. 355 B.C.

Full transcriptTogether, they worked on the famous duplicating the cube problem.

Eudoxus solved it by using curved lines, with his "Kampyle of Eudoxus". http://www.hellenica.de/Griechenland/Mythos/Bild/Archytas.jpg Archytas doubling the cube http://www.karlin.mff.cuni.cz/~rokyta/api/obrazky/dblcube.gif http://www-history.mcs.st-and.ac.uk/Curvepics/Kampyle/Kampyle1.gif a^2x^4=b^4(x^2+y^2) Athens Eudoxus visited Athens for 2 months.

While here, he attended Plato's philosophy lectures.

He was very poor while he lived in Athens, and just to get to the lectures Eudoxus had to walk 11 miles back and forth daily.Thomes Little Heath describes Eudoxus as "... so poor was he that he took up his abode at the Piraeus and trudged to Athens and back on foot each day." in his novel. Egypt Studied here with priests at Heliopolis. This is where Eudoxus became interested in astronomy, making many observations from an observatory between Heliopolis and Cercesura. http://www.iho-ohi.org/wp-content/athens-greece.jpg http://farm3.static.flickr.com/2706/4341988410_0eca737378_o.jpg http://www.mynews.in/News/dailyimage/news/astronomy--med--1.jpg http://clipart.peirceinternet.com/png/telescope1.png Cyzicus Cyzicus was an ancient town of Mysia in Asia Minor.

Eudoxus visited here, starting school. Supposedly, among his students was the famous Aristotle.

He gathered many students of his own during his travels. The success of his teaching may have been a cause of his and Plato's falling out. http://www.mlahanas.de/Greeks/Cities/MinorAsiaCities.gif Return to Cnidus http://www.freefunfiles.com/images/ourfreefunfiles/screensavers/outer-space-vol1.jpg Contributions Mathematics Astronomy Theory of Proportion Comparing possibly irrational lengths without ratios. This helped define the meaning of the equality between two ratios. If a:b and c:d where a, b, c, or d are possibly irrational: i. ma < nb, then mc < nd

ii. ma = nb, then mc = nd

iii. ma > nb, then mc > nd Method of Exhaustion Calculating an area by approximating it by the areas of a sequence of polygons. ex. filling up the interior of a circle by inscribing a polygon with more and more sides. wikipedia.org Eudoxus found that planetary motion could be explained using different axis rotations on a globe. http://www.beyondpluto.net/LYCIA/EudoxanMoon.jpg Each axis revolves around a different rotation of the planet. These represent different periods of time of a rotation: for example one axis represents a 24 hour cycle, or the cycle we know as a day.

http://www-groups.dcs.st-and.ac.uk/~history/Diagrams/Eudoxus.gif The Moon's Spheres 2nd ring is a monthly rotation of the moon's motion through the zodiac. 3rd ring is also a monthly rotation, but slightly angled. This explains motion in latitude. The 5 Visible Planets Venus, Mercury, Mars, Saturn, Jupiter Outermost ring is daily motion, 24 hours. 2nd is the planet's motion through the zodiac. The 3rd and 4th rings trace out a figure 8 hippopede due to retrograde - when a planet seems to slow down before it continues in the zodiac. This idea was later expanded by the mathmetician Archimedes. This was included in Euclid "Elements" Vol. 5. Credit http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Eudoxus.html http://en.wikipedia.org/wiki/Eudoxus_of_Cnidus http://www.math.tamu.edu/~dallen/history/eudoxus/eudoxus.html http://www2.stetson.edu/~efriedma/periodictable/html/Xe.html http://www.mlahanas.de/Greeks/Eudoxus.htm http://scienceworld.wolfram.com/biography/Eudoxus.html http://www.salzgeber.at/astro/moon/aristoteles_Eudoxus.jpg http://www.orbiterwiki.org/images/9/94/MoonThumbTransparent.png http://upload.wikimedia.org/wikipedia/commons/e/e1/Jupiter_(transparent).png Outermost sphere rotates westward every 24 hours:

rising and setting. Eudoxus returned back to Cnidus after his many travels. When he returned, the rulers had been overthrown & democracy established. With no rulers, the citizens asked Eudoxus to write them a constitution. He wrote it & ended up serving on his city's assembly.

He built an observatory and continued his studied until his death in c. 355 B.C.