# Teachers Lesson Plans

## Seeing Math in Art

### -25000

25000 BCE Early geometric designs used and found in archaeological references

### -5000

5000 BCE Egyptians use decimals and geometry for surveying, engineering, agriculture

### -3400

3400 BCE Symbols used for number, although only straight lines, in Egypt

### -2000

2000 BCE Babylonians correctly solve problems with rectangular right prisms and right cylinders.

### -1850

1850 BCE Babylonians document what is known as Pythagorean Theorem.

### -700

700 BCE Indian Sulbasutras created indicating extensive geometric and astronomical understanding used to construct altars for the Veda people

### -575

575 BCE Thales brings Babylonian mathematics to Greece - using geometry to calculate the height of pyramids, distance of ships

### -530

530 BCE Pythagoras teaches and creates a society of learning and religious secrecy, probably the first person to prove Pythagorean Theorem.

### -300

300 BCE Euclid presents systematic development of geometry in *The Elements*.

### -250

250 BCE Archimedes presents formulae for calculating volume of sphere and cylinder, with an approximation of π.

### 628

Brahmagupta uses zero and negative numbers in written work

### 810

Al-Khwarizmi writes work using arithmetic, geography, and astronomy and first work is the source of the word algebra (from al-jabr).

### 1202

Fibonacci writes work that introduces famous sequence of numbers called Fibonacci sequence.

### 1303

Zhu Shijie indicates Chinese understanding of what is now known as Pascal's Triangles and sum of sequences.

### 1482

First mathematics book *Euclid's Elements* printed.

### 1543

Copernicus publishes work that the Sun, not the Earth, is the centre of the Universe

### 1610

Galileo publishes discoveries made with telescopes.

### 1615

Kepler uses elliptical orbits to document conic sections, beginning early introduction to Calculus

### 1626

First use of trigonometric abbreviations (sin, tan, cos) in writing by Girard.

### 1637

Descartes formally applies algebra to geometry, beginning branch now called Cartesian Geometry.

### 1654

Fermat and Pascal exchange letters to work out formal laws for chance and probability.

### 1673

Leibniz demonstrates a calculating machine which can multiply, divide, and extract roots.

### 1678

Newton presents theories of motion, gravity, and mechanics.

### 1706

The Greek letter π used to represent the ratio of circumference to its diameter.

### 1713

Bernoulli publishes work documenting probability models and exponential series.

### 1764

Bayes presents new ideas about chance, now considered Bayesian Theory of Probability.

### 1823

Babbage begins construction of a large machine (engine), to calculate logarithmic and trigonometric functions.

### 1858

Möbius presents a strip of paper with only one side and edge - now known as the Möbius strip.

### 1881

Venn diagrams presented as visual in group theory.

### 1900

Hilbert poses famous problem list as a challenge to the next century.

### 1915

Einstein offers General Theory of Relativity.

### 1920

Sierpinski works on Set Theory and presents closed curve leading to fractals.

### 1936

Turing describes theoretical machine (*Turing machine*) leading to the modern computer.

### 1975

Mandelbrot describes the theory of fractals, more fully described in 1982.