Queen of the Sciences: A History of Mathematics (24 lectures)
David M. Bressoud, Ph.D. Professor, Macalester College
Jaib: means breast, sinus: a cloth to cover cloth, lecture 6, around 10:00
Arabic mistranslation of a transliteration of a Sanskrit word.
1 What Is Mathematics?
2 Babylonian and Egyptian Mathematics
3 Greek Mathematics—Thales to Euclid
4 Greek Mathematics—Archimedes to Hypatia
5 Astronomy and the Origins of Trigonometry
6 Indian Mathematics—Trigonometry Blossoms
Lecture 1 What Is Mathematics?
A mathematician is called Magi, Jesus is supposed to be visited by Persian Mathematicians.
Mathematics is about ideas.
Lecture 2 Babylonian and Egyptian Mathematics
4000 years ago of two math textbooks, 1800BC ag.
The system I use know is very complicated to use position
2, two-strokes with a curve connected them
3, three-strokes with a curve connected them
Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square.
In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if π were transcendental, but π was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π.
The expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible.
The term quadrature of the circle is sometimes used to mean the same thing as squaring the circle, but it may also refer to approximate or numerical methods for finding the area of a circle.
This plimpton 322 contains pythagonren triples.
Completing square
Lecture 3 Greek Mathematics—Thales to Euclid
600 BC- A.D. 400.
This lecture cover from 600 BC - 300 BC when Euclid wrote Elements.
Logos: literally means words.
Hellenistic （公元前 4 至前 1 世纪）希腊化（时期）的of or connected with the Greek history, language and culture of the 4th–1st centuries BC
A
The Museion ( Museum derived from it) came to an end during the life of Hypatia (c, A.D. 370-415, the first woman mathematician) The last references to this center for scholarship occur in the late 4th century and probably coincide with the banning of all pagan temples by Christian Emperor Theodosius I in A. D. 391.
Lecture five Astronomy and the Origins of Trigonometry
Most people think of trigonometry in connection with land measurement, land surveys.
Half of Arc is India mathematicians' design
Retrograde motion
Lecture 6 Indian Mathematics—Trigonometry Blossoms
zero was invented about between A. D 300 and 600/700. Astronomer Brahmagupta explained how to add and subract zero and how to multiply by zero.
Raduis of 3438 = 360 * 60 / 2 * pi
Write about how to find square root of 2, so that area of the altar will be increased by 2, or cube root of 2 so that volume will be increased by 2.
How I solve it
linear interpolation , quadratic interpolation
Diophantine equation
The ratio of two integers that satisfy the equation gives a good approximation to square root of 8 is 2.82842712475.
17/8 = 2.125, 3363 / 1189 = 2.828427
Ujjain was destroyed. Astronomers moved to Kerala.
