106 midterm
Instructor: Peter Petersen
Date: Feb 26, 2016
Place: MS 5200
Name
Student number
Section
Instructions:
(1) First read all questions.
(2) Each question carries a weight of 10 points.
(3) No electronic devices, textbooks, or cheatsheets are allo
EXERCISES
1. Prove two theorems attributed to Thales and tell, with reasons, whether or not you think
he may have used similar reasoning.
Prove the Pythagorean theorem. Do you think Pythagoras used your method? Explain.
3. Theon of Smyrna, a Neoplatonist
1. Describe the sources Euclid probably used in writing the Elements; justify your presump.
tions.
2. Which of the thirteen books of the Elements do you regard as the most important? Justify
your answer.
3. Which of the thirteen books of the Elements do y
EXERCISES
l.
2.
3.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Describe the evidence on which our estimate of Egyptian mathematics is based. Do you
think that this is likely to be altered by the discovery of new documents? Explain.
Do you think that astronomy was
EXERCISES
- 1, The names of Aristotle, Euclid, Archimedes, and Apollonius are associated respectfvély; I,
with those of four powerful rulers—Alexander, Ptolemy, Hiero, and Attalus. Tell where these
men ruled and in what connection their na
Chapter 10.8
James Gregory
Scotland (1638)
mathematician and astronomer
first achievement:invention of the reflecting telescope in his book Optica promota(failed),
Newton succeed
1664-1668 study math in Italy
Teacher Stefano degli Angeli-Vera circuli
DIFFERENCES AND INTERPOLATION
PETER PETERSEN
Consider a sequence
a0 , a1 , a2 , ., an , .
Define the sequence of first dierences as
a0 = a1
a0 ,
a1 = a2
a1 , .,
an = an+1
an , .
the second dierences
2
a0 =
a1
a0 = a2 2a1 +a0 , .,
2
an =
an+1
an = an+2 2an
106 midterm
Instructor: Peter Petersen
Date: Jan 29, 2016
Place: MS 5200
Name
Student number
Instructions:
(1) First read all questions.
(2) Each question carries a weight of 10 points.
(3) No electronic devices, textbooks, or cheatsheets are allowed.
(4)