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A systematic study of numbers and forms. |
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In mathematics, Thales used geometry to calculate the heights of pyramids and the distance of ships from the shore. He is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. He is the first known individual to whom a mathematical discovery has been attributed. |
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Paleolithic Age: (Stone Age) |
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From 2 million BC → 10,000 BC
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From 50,000 BC → 30,000 BC |
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Wolf Bone was found in old Czech Republic. There were vertical notches in the bone (55) when it was only 7 inches long. The vertical notches were in groups of 5
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When was the discovery of A discovery of the Ishango Bone (Baboon bone)? |
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From 30,000 BC → 20,000 BC |
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From 10,000 BC → 4,000 BC |
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| Positions or place values, is between 0 and n-1 where n is equal to the base. |
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( Quinonary System) with 5 digits 0-4 |
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| Binary system where digits are 0-1 |
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Flourished in America and Guetamala and Bellese |
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| What Base system did the Mayans have? |
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| A Base 20 or Vigesimal system. |
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| What were the Three rules of the Mayan Numeral System? |
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1. All Numerals were written vertically
2. Highest power at top.
3.From the 202 digit on, one factor of 20 is replaced by 18.
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Maya codices are folding books stemming from the pre-Columbian Maya civilization, written in Maya hieroglyphic script on Mesoamerican bark cloth, made from the inner bark of certain trees, the main being the wild fig tree or amate. |
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the most important of the few that survive. |
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| What are the four codices left from the mayans? |
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Dresden Codex:
Paris Codex
Madrid Codex
Grolier Codex |
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- Diego de Landa Calderón was a Spanish bishop of the Roman Catholic Archdiocese of Yucatán.
- He left future generations with a mixed legacy in his writings, which contain much valuable information on pre-Columbian Maya civilization, and his actions which destroyed much of that civilization's history, literature, and traditions.
- He is a major figure in the so-called "Black Legend"
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| What are the two different types of Egyptian Scripts? |
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| Heirtic and heirogylphics |
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The most abundant script seen on artifacts.
They weren't pictures, they were more of lines and dots.
Used more by the priests
Would use unit fractions.
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- Created as a commemorative for a battle that the Egyptians won.
- Base is cast out of bronze.
- Recorded what the Egyptian won from the battle, engrossed into the bronze
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- A stone that was uncovered in the year 1879.
- Discovered by Napoleon generals.
- The shape of the stone is broken, very heavy.
- Preserved at the British museum
- Had writing on it, in three sections with script
- Top script was hieroglyphics
- Middle was Demotic
- Bottom was Greek
- All three sections were the same script, just written in different perspectives.
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- Was the original scientist who deciphered Egyptian Hieroglyphics
- Very well known in France, on dollar bills and on postage stamps.
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- Mostly used for scripts in Egyptian
- Were considered as a book
- Written on both sides
- Thousands of these scrolls have been preserved in universities and museums
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Moscow (Golemischeu) Papyrus
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- A scroll located in Moscow
- Purchased from Egypt in 1893
- Dimensions are 3 inches wide and 18 feet long
- A number of mathematical problem (25) that was written on the scroll.
- The date of the papyrus was said to be around 1890 BC
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- V = h/3(a2 + ab + b2)
- Located in the Moscow Scroll.
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| Rhind Mathematical Papyrus |
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- Dimensions were 13 inches by 18 feet.
- Contains 84 mathematical problems
- Have tables dispersed throughout the papyrus
- The chief scroll which holds most of the Egyptian Math
- Dates back to 1600 BC
- Written by Ahmes who was a scribe that worked with the Egyptian Mathematicians.
- He stated that it was already 200 years old and that he just copied it. So it was originally made in 1800 BC.
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- distinguished by its wedge-shaped marks on clay tablets, made by means of a blunt reed for a stylus. The name cuneiform itself simply means "wedge shaped", from the Latin cuneus "wedge" and forma "shape," and came into English usage probably from Old French cunéiforme.
- Millions preserved throughout the country
- Only 100-200 are mathematical
- Only few are significantly perceived as a mathematical asset.
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| What Base system do the Babylonians use? |
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an Austrian American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages. By studying clay tablets, he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age. |
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The Behistun Inscription, is a multi-lingual inscription and large rock relief on a cliff at Mount Behistun in the Kermanshah Province of Iran, near the city of Kermanshah in western Iran. It was crucial to the decipherment of cuneiform script. |
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- This tablet is a round school tablet of unknown provenance from the Old Babylonian period. It has a picture of a square with both diagonals drawn in. On one side of the square is written the number 30, along one of the diagonals is the number 1,24,51,10 and below it is 42,25,35.
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a diagram of a circle with the numbers 3, 9 and 45. The 45 represents the area of the circle, while 3 is the circumference. The usual rule for computing the area of a circle in Old Babylonian mathematics is A=C^2/12, or rather A=5C^2 as 5 is the reciprocal of 12. |
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