i mhf3404- history of mathematics florida...
TRANSCRIPT
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Answer all 10 questions. Provide all reasoning and show all WO
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ing. An unjustified answer willreceive little or no credit. Begin each question on a separate page Parts (a) and (b) should be doneon the same page if possible. You may write on both sides of th paper.
1. (a) Multi pIy 15 by 11, & (b) Divide 247 by 19, by USin~the Egyptiau Doubling Method.
2. Find the 3rdrational approximation to the square-root of 2 by using the Babylonian Halving
Method and starting with 1 as the O-thapproximation. \,
I(a) Find a Pythagorean Triple which contains 11 as its 1mallest term. (b) Is a there a
Pythagorean Triple with 4 as its smallest term? (Justify yjr answer.)I
Findthe greatestcommondivisorof 171 aud 132by usingfUc1id's Algorithm.,
Let ABC be a Triangle with angle ABC having measure leS
tthan 90 degrees. Let AD be
the perpendicular to BC from A which meets BC in D. Assu ing the Pythagorean Theoremfor Right Triangles, prove that AC2 = AB2 + BC2 - 2.B .BD.
MHF3404- HISTORY OF MATHEMATICSTEST #1 - Spring '09
FLORIDA INTL UNIV.TIME: 75 min.
3.
4.
5.
6.Find the first 4 digits of the decimal expansion (3 decimal p~aces)ofthe square-root of 10
by using the Digit by Digit Algorithm which is essentially dre to Theon of Alexandria.
7. (a) How many days were there in the year 1500CE in Rome'
tnd how many days will there
be in the year 2100 CE in Rome? (Explain how you got yo r answer.) (b) Explain whyPope Gregory found it necessary to let the year 1582 CE hav only355 days.
8. (a) Define what are Axioms, Postulates, Hypothesis, & Theolems in the way that Aristotleunderstood them. (b) Justify why the curved surface ar~a of a conical frustrum is
(Pi).(R]+R2).Lbyusingthe methodof infinitesimalslicing.\,
(a) Find the volume of the solid by revolving the disk: X2+
~
~ 9, about the line x = 5.(b) Find the centroid of the semicircular curve with equat on: x2 + i =a2 & x non-negative, by using Pappus' Theorem and the fact that the surf; ce area of a sphere of radiusa is 4/-l(eJ;z,. [No integration is necessary to solve this pr blem.]
9.
10.
I
(a) Define what is the curve known as the Quadratrix ofHipp~s.
Hippias can be used to trisect an angle and to square the circ~e.solutions unsatisfactory? I
(b) The QuadratrixofIn what ways are these
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