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Calculus 4E Chptr 4
C 4E Ch 4 - The Platonic-Pythagorean Project before the Scient. Rev.
| Question | Answer |
|---|---|
| the general project of uncovering the mathematical order of nature that hides behind chaotic appearance | The Platonic-Pythagorean Project |
| one of the main goals of science | to understand change in mathematical terms |
| What does it mean to quantify motion? | to attach numbers to it |
| Describing space, time, and numbers is difficult due to problems which arise from the concepts of | continuity and infinity. |
| The concept of instantaneous speed seems incoherent because no distance can be traveled in an ________________. | instant |
| Eudoxus | Plato's student, d, 355 BC, the first to answer Plato's challenge, used spheres to describe the motions of the heavens |
| Plato & Eudoxus did not believe the spheres physically existed; and they only described _________ was happening, not ___________. | WHAT . . . (not) why |
| The sign above the entrance to Plato's Academy | "Let no one ignorant of GEOMETRY enter here." |
| Euclid's Elements | ancient Greek mathematics text, contains no numbers, only theorems and proofs about shapes; the West's main mathematical text for 2,500 years |
| It is significantly easier to use mathematics to describe the motion celestial objects than it is to mathematically describe | the motion of earthly objects. |
| Aristotle | d. 323 BC, sought to know what caused things to move; developed discipline of Logic, denied there was a world of Forms |
| what science has been called for most of Western history (until the 1800s) | natural philosophy |
| 4 elements ancient Greeks believed composed terrestrial objects | earth, air, fire, & water |
| Plato's proposed 5th essence | ether |
| Aristotle's 4 "causes" | the 1) material, 2) efficient, 3) formal, & 4) final causes; Aristotle's solution to the problem of change |
| nature (according to Aristotle) | dictated by an objects composition, what terrestrial objects attempt to find their rest in |
| Greek word for nature | physis |
| "Ignorance of motion is ignorance of nature." | medieval Scholastics' saying |
| discipline that studies forces acting on stationary objects | statics |
| Archimedes | d. 212 BC, known for his mathematical description of the forces acting on a lever |
| "Eureka!" | "I found it!" |
| equilibrium | concept of balance |
| Archimedes discovered that the ___________ ______________keeping an object afloat is equal to the weight of the liquid that the floating object displaces. | upward force |
| hydrostatics | studies forces acting on stationary objects in water or some other fluid |
| Archimedes' Law of the Lever: | "Two magnitudes balance at distances reciprocally proportional to the magnitudes." |
| Claudius Ptolemy | great Egyptian astronomer & mathematician, introduced trigonometry to Western science, wrote Almagest, d. 168 AD |
| Scholasticism | a combination of Aristotle's teachings with Christianity |
| Sir Isaac Newton | eventually replaced Aristotle as king of science |
Created by:
MrsHough
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