Group 1 Flashcards
- region in Mesopotamia
- modern-day Iraq
- called the “Cradle of Civilization”
Sumer
Sumer is called the “__ _ __”
Cradle of Civilization
Sumer is modern-day __
Iraq
- earliest known writing system
- created by the Sumerians
cuneiform script
cuneiform script was a __ writing system
pictographic
When did Sumer’s society stabilize and advance in agriculture
6th millenium BCE
Sumerian mathematics was first mostly a response to what
governmental requirements for measurement of land plots, taxing of individuals, etc.
When is the first recorded use of abacus
2700 - 2300 BC in Mesopotamia
Where is the first recorded use of abacus
Mesopotamia
numeral system with 60 as its base
Sexagesimal Numeral System
Sumerians were the first civilization to use a __ __ numeral system
place value (numeral system)
Sumerians’ place value numeral system was developed and passed on to the
ancient Babylonians
Who created a circle character for zero
Babylonians
Zero was another groundbreaking mathematical idea that the __, __, and __ did not have
- Egyptians
- Greeks
- Romans
oldest known evidence of humans using applied geometry
Babylonian clay tablet
When is the oldest known evidence of humans using applied geometry made
1900 - 1600 BCE
Babylonian clay tablet, notable as containing an example of Babylonian mathematics.
Plimpton 322 Clay Tablet
When did the early Egyptians settle along the fertile Nile valley to record the lunar phases and seasons
6000 BCE
The Egyptians settled along the fertile Nile valley to record the lunar phases and seasons for what purposes
religion and agricultural purposes
What did the Pharaoh’s surveyors use as a basis to measure land and buildings
body parts
body part used to measure width
palm
body part used to measure cubit
elbow to fingertips
- little pictures that represent words or numbers
- used around 3000 BCE
Hieroglyphic Numbers
When were hieroglyphic numbers used
around 3000 BCE
Hieroglyphic numbers is a base __ system
10
Hieroglyphic numbers:
10 is shown by
drawing of a hobble for cattle
Hieroglyphic numbers:
100 is represented by
coil of rope
Hieroglyphic numbers:
1,000 is represented by
drawing of lotus plant
Hieroglyphic numbers:
10,000 is represented by
a finger
Hieroglyphic numbers:
100,000 is represented by
tadpole or frog
Hieroglyphic numbers:
1,000,000 is represented by
a god with arms raised above his head
- oldest mathematical text in ancient Egypt so far
- dates from the Egyptian middle kingdom around 2,000 - 1,800 BCE
Moscow Papyrus
Moscow Papyrus dates from the Egyptian middle kingdom around _____
2,000 - 1,800 BCE
- kind of instruction manual in arithmetic and geometry
- gives explicit demonstration of how multiplication and division was carried out at the time
- scroll about 6 meters long and 1/3 meter wide
- written around 1650 BCE by scribes Ahmes
Rhind Papyrus
Rhind Papyrus measurement
- 6 meters long
- 1/3 meter wide
When was the Rhind Papyrus written
around 1650 BCE
Who wrote the Rhind Papyrus
scribe Ahmes
Rhind Papyrus is a kind of instruction manual for what
arithmetic and geometry
Rhind Papyrus gives an explicit demonstration of what
multiplication and division carried out at the time
- dates from around 1300 BCE
- shows that Egyptians could order algebraic (quadratic equations)
- where the Pythagorean Theorem was written on
Berlin Papyrus
Berlin Papyrus dates from around what
1300 BCE
What does the Berlin Papyrus show
Egyptians could order algebraic (quadratic) equations
What was written on Berlin Papyrus
Pythagorean Theorem
- base 10 system similar to the earlier Egyptian
- with symbols for 1, 5, 10, 50, 500, and 1000
Greek Numeral System
Timeline of the Greek Numeral System
450 BCE - 7th Century
Greek Numeral System is a base __ system
10
Greek Numeral System has symbols for what
1, 5, 10, 50, 500, and 1000
The ancient Greek numeral system is known as
Attic or Herodianic numerals
- one of the Seven Sages of Ancient Greece
- considered to have been the first to lay down guidelines for the abstract development of geometry
Thales
What did Thales establish
- Thales’ Theorem
- Thales’ Intercept Theorem
if a triangle is drawn within a circle with the long side as a diameter of the circle, then the opposite angle will always be a right angle
Thales’ Theorem
about the ratios of the line segments that are created if two intersecting lines are intercepted by a pair of parallels
Thales’ Intercept Theorem
What are the Three Classical Problems
- Squaring (quadrature) of the circle
- Doubling (duplicating) of the cube
- Trisection of an angle
wrote “The Elements”
Euclid
- compilation of theorems, axioms in Algebra and postulates and theorems in Geometry
- written by Euclid
The Elements
The Elements was used from ___
300 BCE - 200 AD
idea of proof, and the deductive method of using logical steps to prove or disprove theorems
- Pythagoras
- Plato
- Aristotle
- imposed “god is a number” or “all is number” in his scholars
- complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth
Pythagoras
for any right-angled triangle, the square of the length of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the square of the other two sides (or “legs”)
Pythagorean Theorem
Pythagorean Theorem equation
a^2 + b^2 = c^2
What did Pythagoras impose
“god is number” or “all is number”
- One of ancient Greece’s most important patrons of mathematics.
- founded an Academy in Athens in 387 BCE making Pythagoras as his inspiration. His academy entrance says: “Let no-one ignorant of geometry enter here”.
- His Academy taught Mathematics as a branch of Philosophy.
- also known as the “maker of mathematicians”
Plato
When did Plato establish his academy in Athens
387 BCE
Where did Plato establish his academy
Athens
What does Plato’s academy entrance say
“Let no-one ignorant of geometry enter here.”
Who is Plato’s inspiration for his academy
Pythagoras
Plato’s academy taught mathematics as a branch of what
Philosophy
Plato is also known as the “__ _ __”
maker of mathematicians
Platonic Solids
- Tetrahedron
- Octahedron
- Icosahedron
- Cube
- Dodecahedron
Who discovered the octahedron and icosahedron
Theaetetus (contemporary of Plato)
