Archimedes

We can only speculate about the effect that the "method" would have had on the development of calculus had it been known in the 16th and 17th centuries. See also. As a result, his mechanical method was lost until around 1900, after the arithmetization of analysis had been carried out successfully. Some of Rivera's accomplishments include:. Many of his works were lost when the library of Alexandria was burnt (twice actually) and survived only in Latin or Arabic translations. However, Rivera is permitted to use the number due to a grandfather clause, and he is the last active Major League player to wear the number. During the Middle Ages the mathematicians who could understand Archimedes' work were few and far between. His uniform number is 42, which has been retired by all Major League Baseball teams since 1997 in honor of Jackie Robinson.

He and his contemporaries probably constitute the peak of Greek mathematical rigour. As Rivera enters a game in Yankee Stadium, the song "Enter Sandman" by Metallica is played on the loudspeaker system. Archimedes' works were not widely recognized, even in antiquity. Rivera's signature pitch is his cut fastball, or cutter, which he mixes with both a four-seam and two-seam fastball. Pappus of Alexandria writes that Archimedes had written a practical book on the construction of such spheres entitled On Sphere-Making. He won the World Series MVP Award in 1999, when which the Yankees swept the Atlanta Braves in four games and Rivera earned two saves. For some time this was assumed to be a legend of doubtful nature, but the discovery of the Antikythera mechanism has changed the view of this issue, and it is indeed probable that Archimedes possessed and constructed such devices. He donated his 2001 trophy to the New York City Fire Department, and the trophy is on permanent display at the FDNY's Brooklyn headquarters.

He credits Thales and Eudoxus for constructing these devices. Rivera has won the Rolaids Relief Man of the Year Award three times, in 1999, 2001, and 2004. One device mapped the sky on a sphere and the other predicted the motions of the sun and the moon and the planets (i.e., an orrery). In 2005, Rivera converted 31 consecutive save opportunities, his career record, in addition to his save in the 2005 All-Star Game in Detroit. Apart from general physics he was an astronomer, and Cicero writes that the Roman consul Marcellus brought two devices back to Rome from the sacked city of Syracuse. In 2003, he would have arguably his best postseason performance ever, when he pitched 3 shutout innings in a Game 7 victory over the powerful Boston Red Sox. Using only ancient Greek geometry, he also gave the equilibrium positions of floating sections of paraboloids as a function of their height, a feat that would be taxing to a modern physicist using calculus. Since then, Rivera has been less consistent in the postseason, but Rivera's performance after blowing that save is second only to his performance before that game.

He was the first to identify the concept of center of gravity, and he found the centers of gravity of various geometric figures, assuming uniform density in their interiors, including triangles, paraboloids, and hemispheres. Rivera's most infamous moment in the postseason occurred in Game 7 of the 2001 World Series, when he blew the save in the bottom of the 9th inning despite striking out the side the previous inning. (He famously discovered the latter when he was asked to determine whether a crown had been made of pure gold, or gold adulterated with silver; he realized that the rise in the water level when it was immersed would be equal to the volume of the crown, and the decrease in the weight of the crown would be in proportion; he could then compare those with the values of an equal weight of pure gold). From 1997 to 2001, Rivera converted 23 postseason saves successfully and pitched 34 consecutive scoreless innings in the postseason, both Major League records. He invented the field of statics, enunciated the law of the lever, the law of equilibrium of fluids and the law of buoyancy. Rivera's postseason dominance played a key role in the Yankees' four championships in five years in the late 1990s. Archimedes is probably also the first mathematical physicist on record, and the best before Galileo and Newton. Rivera has been especially overpowering in the postseason, in which his lifetime ERA of 0.75 is the Major League record.

He proved that the area and volume of the sphere are in the same ratio to the area and volume of a circumscribed straight cylinder, a result he was so proud of that he made it his epitaph. He has been one of the most consistent, dependable relief pitchers in the Major Leagues during his tenure as a closer for the Yankees. Archimedes also gave a quite different proof of nearly the same proposition by a method using infinitesimals (see "How Archimedes used infinitesimals"). When Wetteland left the team following that season (in which they won the World Series), Rivera became the Yankees' closer and has remained so through 2005. Essentially, this paragraph summarizes the proof. Despite playing in a position that rarely gets respect, Rivera still managed to come in third for the Cy Young Award voting, behind twenty-game winners Pat Hentgen and teammate Andy Pettitte, respectively. If the first term in this series is the area of the triangle in the illustration then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines in the illustration. During that season, if the Yankees were leading after six innings, they were nearly assured of victory due to the stellar pitching of both relievers.

In the process, he calculated the oldest known example of a geometric series with the ratio 1/4:. In 1996, he served primarily as a set-up man for the closer John Wetteland. The vertex must be so placed that the two horizontal distances mentioned in the illustration are equal.). Born in Panama City, Panama, his rookie season in the Major Leagues was 1995, in which he made a limited number of appearances. "Height" means the length of the segment parallel to the axis from the vertex to the base. Mariano Rivera (born November 29, 1969) is a relief pitcher for the New York Yankees, a surefire future Hall of Famer considered by many to be "The Greatest Closer of All-Time.". The "base" is any secant line, not necessarily orthogonal to the parabola's axis; "the same base" means the same "horizontal" component of the length of the base; "horizontal" means orthogonal to the axis. List of players from Panama in Major League Baseball.

(See the illustration below. Yankees' all-time leader in saves and appearances. He proved that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height. 4-time World Series champion. He was the first, and possibly the only, Greek mathematician to introduce mechanical curves (those traced by a moving point) as legitimate objects of study. 7-time All-Star. He did not call this ratio π but he gave a procedure to approximate it to arbitrary accuracy and gave an approximation of it as between 3 + 1/7 and 3 + 10/71. Only reliever to win ALCS (2003) and World Series MVP (1999) awards.

He proved that the ratio of a circle's perimeter to its diameter is the same as the ratio of the circle's area to the square of the radius. Most saves in World Series play (8). To what extent he actually had a correct version of integral calculus is debatable. Recorded 11 2-inning saves in the postseason (as of 2003). He devised a heuristic method based on statistics to do private calculation that we would classify today as integral calculus, but then presented rigorous geometric proofs for his results. Holds record for 34 1/3 consecutive scoreless innings pitched in postseason. In a civilization with an awkward numeral system and a language in which "a myriad" (literally "ten thousand") meant "infinity", he invented a positional numeral system and used it to write numbers up to 10⁶⁴. One of only 6 pitchers to record at least 53 saves in a season.

In creativity and insight, he exceeded any other mathematician prior to the European Renaissance. One of only 8 pitchers to record at least 50 saves in a season. The Greeks said that he was killed while drawing an equation in the sand, and told this story to contrast their high-mindedness with Roman ham-handedness; however, it should be noted that Archimedes designed the siege engines that devastated a substantial Roman invasion force, so his death may have been out of retribution. Only 3rd pitcher in history to notch 300 saves with one team. Archimedes was killed by a Roman soldier in the sack of Syracuse during the Second Punic War, despite orders from the Roman general, Marcellus, that he was not to be harmed. 5th all-time in career saves (371), 2nd all-time among active pitchers (as of September 1, 2005). After a number of experiments, whereby the hosts of the program tried burning a model wooden ship with a variety of mirrors, they concluded that the enemy ships would have had to have been virtually motionless and very close to shore for them to ignite, an unlikely scenario during a battle. Only 2nd closer in history to record 40 saves in 5 different seasons.

This popular legend was tested on the Discovery Channel's Mythbusters program. Second-best save conversion percentage of closers with at least 150 saves (87.5%) (as of 2004). It is said that he prevented one Roman attack on Syracuse by using a large array of mirrors (speculated to have been highly polished shields) to reflect sunlight onto the attacking ships causing them to catch fire. Lowest career ERA of closers in top 50 of career saves (2.35) (as of 2005). One of his inventions used for military defense of Syracuse against the invading Romans was the claw of Archimedes. Most postseason saves of all-time (25) (as of 2004). He has also been credited with the possible invention of the odometer during the First Punic War. Lowest postseason ERA of all-time (0.75) (as of 2004).

He is reputed to have held the Romans at bay with war machines of his own design; to have been able to move a full-size ship complete with crew and cargo by pulling a single rope; to have discovered the principles of density and buoyancy, also known as Archimedes' principle, while taking a bath (thereupon taking to the streets naked calling "eureka" - "I have found it!"); and to have invented the irrigation device known as Archimedes' screw. Archimedes became a popular figure as a result of his involvement in the defense of Syracuse against the Roman siege in the First and Second Punic Wars. . He is considered by some math historians to be one of history's greatest mathematicians, along with possibly Newton, Gauss and Euler.

Archimedes (Greek: ΑΡΧΙΜΗΔΗΣ) (287 BC–212 BC) was an Ancient mathematician, physicist, engineer, astronomer and philosopher born in the Greek seaport colony of Syracuse. The Acorn Archimedes. Asteroid 3600 Archimedes, named in his honour. Archimedes crater on the Moon.

Given Archimedes's prodigious output as an engineer, Plutarch's often quoted comments on him seem hard to believe by modern historians. It has also been suggested that this statement merely reflects the prejudices of Plutarch and his peers, influenced by Platonic beliefs in pure reasoning and deduction over experimentation and inductive processes. "...but regarding the work of an engineer and every art that ministers the needs of life as ignoble and vulgar, he devoted his earnest efforts only to those studies the subtlety and charm of which are not affected by the claims of necessity." Plutarch, possibly explaining why Archimedes produced no writings that describe precisely the design of his inventions. 95)¹.

"Perhaps the best indication of what Archimedes truly loved most is his request that his tombstone include a cylinder circumscribing a sphere, accompanied by the inscription of his amazing theorem that the sphere is exactly two-thirds of the circumscribing cylinder in both surface area and volume!" (Laubenbacher and Pengelley, p. "The Method". The Sand Reckoner. Archimedes' Cattle Problem.

Stomachion. The Quadrature of the Parabola. On Floating Bodies (2 volumes). On Conoids and Spheroids.

On the Sphere and The Cylinder. On Spirals. On the Equilibrium of Planes (2 volumes).