Math History
Terms
undefined, object
copy deck
-
Heron
1. Where from?
2. What were his two works called?
3. What did he find out? -
1. an Egyptian with Greek training
2. Geometric (problems on mensuration) and Mechanical (descriptsion of ingenious mechanical devices)
3. A method of finding a sqrt approximation of a nonsquare interger - Heron's method of finding square root approximation.
-
If n=ab, then sqrt(n) is approximated by (a+b)/2, then the approximation improving with the closeness of a tob.
a(1) = first guess
a(2) = [a(1)+n/a(1)]/2
a(3) = [a(2)+n/a(2)]/2 - Use Heron's method of sqrt approxmation to find the square root of 54.
- 7.35
- What are the three stages in historical development of algebraic notation ?
-
1. Rhetorical Algebra
2. Synocopated Algebra
3. Symbolic Algebra - Rhetorical Algebra
- Solution of a problem written without abbreviations of symbols
- Syncopated Algebra
- Abbreviations are adopted for some of the more frequrently reoccuring quantities and operations
- Symbolic Algebra
- Solutions appear largely in a mathematical shorthand made up of symbols having little apparent connection with teh entities they represent.
- Three works of Diophantus
-
1. Arithmetica
2. On Polygonal Numbers
3. Porisms - Diophantine Problems
- Intermediate algebraic problems in which one must find only the rational solutions
- How do you solve a Diophantine Equation?
- a is similar to b (mod m) if and only if a/m, b/m have the same remainder
- What work did Ptolemy Soltec write?
- "Al-majest"
- State Ptolmey's Theorem
- In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the prodcuts of the two pairs of opposite sides
- What is Ptolemy's method of square root?
- Refer to book, pg 177
- What are the two types of Liberal Arts?
-
1. Quadrivium
2. Trivium - What are the four Quadrivium?
-
1. Arithmetic
2. Music
3. Geometry
4. Astronomy - What are the Three Trivium?
-
1. Logic
2. Grammar
3. Rhetoric