Homework for Mat 406/5401
August 25 – Discussion included: where to find the syllabus; difference between number and numeral; properties of
numeration systems; names of different base numeration systems; how to write Mayan numerals; how to write
Egyptian numerals; and how to add/subtract Egyptian numerals. Homework: READ Chapter 1, Read the syllabus, and
Section1.2 problems 1-4 every other part if there are multiple parts.
August 27 – Discussed: different writing materials on which mathematics was recorded, traits of Egyptian and
Babylonian mathematics, numerals in sexagesimal notation, dates of earliest papyri (Moscow and Rhind) , and kinds of
information found on tablets. Homework: 1.2 – 11, 12, 13 every other part. 1.3 4, 13, 14, 15.
August 30 – Discussed unit fractions of the Egyptians, using the table from the Rhind Papyrus, and the “splitting”
algorithm. Discussed multiplication using duplication. Homework: Section 2.1 – 1, 11, 12a and 14. Assignments for
philosophy of mathematics were given. Reports are due September 10 (written and oral). Students are to find
“uses of number” from Numbers by Friday.
September 1 – Discussed Fibonacci’s method of decomposition, four special versions (in homework problems), and
solving equations by the method of False Position. Discussed the dates from artifacts. Homework: Section 2.3 - 2(as
many as you need), 6, 7, 9, 12b, 16 (if you need it) 19 and 20.
September 3 – Collect the homework – students selected two parts that had no answers in the back. Discuss
decomposition of a frustum of a square pyramid to derive the formula for its volume. Discussed pi values for Egyptians,
Babylonians, and even the Hebrews from 3000 BC to about 650 BC. Looked at several formulas for volume that were
used in this time period. Homework: Section 2.3 – 21 and 22. Section 2.4 – 1a, 2a, 9a and b if you have time. Finish
reading Chapter 2 – reading lightly.
September 8 – Gave homework hints about # 19 from 2.3 and # 9a from 2.4. Discussed how Babylonians solved a
special quadratic equation, and three different systems of linear and quadratic equations. Homework: Verify that the
Babylonian quadratic formula used is equivalent to the one we use today. Section 2.5 – 4, 6, and 12. Moved the
deadline for reports to Monday September 13.
September 10 – Discussed last section of Chapter. Set Test date for 20th of September. Answered questions about
homework. Homework: Section 2.5 - #13 – work a couple of parts. Section 2.6 work 2 of the first four problems.
Google to see when & why the prime meridian is where it is. Verify the formula for the volume of a frustum of a square
pyramid.
September 13 – Discussed Ptolemy’s Table of Chords, Thales and the early Greeks. Students should have read through
section 3.1 – Test is Monday, September 20 on Chapters 1, 2, and section 3.1
September 15 – Reviewed what Thales knew. Began the discussion of the Pythagoreans, a video about the
Pythagoreans was played; saw a demonstration of a Pythagorean cup. Read about the Pythagoreans; be prepared to ask
any questions that you want to on Friday.
September 17 – Discussed when Thales and the Pythagoreans lived in reference to the Old Testament names students
know. Discussed prime, perfect, abundant, deficient, and amicable (friendly) numbers. Discussed how the
Pythagoreans might have constructed segments that have irrational numbers for the measure of their length.
Homework: TEST ON MONDAY 1-section 3.1. BY Wednesday, using a given segment whose length you call “one”,
construct the √2 ,√3, and √5. Discern which of the natural numbers 1-15 are perfect, abundant or deficient. READ
about Jacob and Esau’s reconciliation. How many critters were in the first herd that Jacob sent to Esau?
September 20 – TEST
September 22 - Tests and philosophy reports were returned. Discussion included friendly numbers, triangular
numbers, square numbers and several theorems about the figurate numbers. Homework: Section 3.2 – 3, 4, 6, 11a,
and find the first five Pythagorean triples generated by the forms used by Pythagoras, Plato, and Euclid.
September 24 – Discussed Athens a bit, the Platonic solids and Greek mathematicians. Homework: Section 3.2 - 8 and
another part of 11. Reports assigned today are due October 6.
September 27 – Discussed three famous problems of antiquity. Students should know what the problems were, who
created a solution, and what the solution was. Discussed the technique in Problem 8 on page 131 of constructing the 4th
proportion. Suggested students read #3, 4, 6, and 7 from Section 3.4 to see solutions proposed to the three famous
problems. Homework: Section 3.3 – 1, 4, 5b, read #17.
October 6 – Three students gave their reports. Discussed construction of a geometric mean, and where the arithmetic
mean is. Discussed contents of Euclid’s Elements. Homework: Section 4.2 – 7-11 and practice construction of the
geometric mean. Read about constructing the golden section/golden ratio (φ) and what its value is.
October 8 – Discussed number theory concepts included in Euclid’s Elements. Corrected what is a typing error. TEST ON
SECTIONS 3.2 THROUGH CHAPTER 4 IS SCHEDULED FOR OCTOBER 20. Homework: handout sheet on constructions,
Construct a regular pentagon using the method in the text. Finish the proofs that were assigned from last class. Section
4.3 -1, 6, 7, 11, 16 parts a and c at least.
October 11 – Quiz on construction with open notes. Discussed :another way to construct a regular pentagon;
Eratosthenes’ accomplishments and his sieve; and works of Archimedes. Since test is next week, the section of Chapter
5 (5.2) that has Diophantus will be included on the test. Homework: Pick up a sheet outside Dr. Floyd’s door to use to
complete the Sieve of Eratosthenes to identify primes less than 300. Section 4.3 – 8, 14, 15 (a couple), 24. Section4.2
correction, homework should have said 7-10.
October 13 – Returned quiz on construction. Collected the Sieve that was homework. Discussed Archimedes further
and Apollonius. Attention was called to several formulas in the exercises and solutions to the four problems that are
discussed in the exercises of Chapter 4. Homework: Read Chapter 5 through Section 3. Verify that Heron’s formula
works on triangles that you draw and find the area using multiple formulas that you know. Test Next Wednesday
covers Sections 3.2 through 5.3.
October 15 – Discussed Archimedian Solids, Diophantine equations, and Diophantus’ Arithmetica. Homework: Section
5.3 - Work 3 or 4 of the problems 1-12 (from Arithmetica), 14 and 15 when possible. Tests will be administered by
appointment Wednesday or Thursday.
October 18 - Discussed topics/sections for the test this week. Scheduled test times for those students present.
Discussed contributions of commentators and contributions from India. No homework, only notes.
October 20 – Discussed contributions of Chinese and Arabs to mathematics. No homework, scheduled tests.
October 22 – Completed discussion of Arab contributions, completing the square by their technique and assigning the
third project. Homework from Chapter 5 includes – READ THE CHAPTER LIGHTLY; Problems from Section 5.3 – 16, 17,
18 and 21, Section 5.4 – 2 and read #3, Section 5.5 – 1, 2a, 3, 5, 12, 14 and 18. Expand (𝟑𝒙 − 𝟐𝒚)𝟕 using any method
you know OR the Arab method discussed today. Third projects were Ellipse – Katie Beth, parabola – Ori, hyperbola –
Brittany, and Zach yet to draw a topic. NEXT TEST WILL COVER CHAPTERS 5.3 – 7 probably November 5th?