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they are measure words/terms that are included when # words are spoken with nouns...They make qualifications- for ex: 5 feet of grass
European scholars saw the classifiers as proof that the illiterate ppl did not understand the concept of numbers and were prmitive because numerical classifiers came before number systems. |
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Quipu or khipu (sometimes called talking knots) were recording devices used in the Inca Empire
ere capable of performing simple mathematics, basic arithmetic operations such as adding, subtracting, multiplying, and dividing information for the indigenous people. This included keeping track of mita, a form of taxation.
In the Aschers' system a fourth type of knot--figure-of-eight knot with an extra twist--is referred to as "EE". A number is represented as a sequence of knot clusters |
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| base 10 base 60 think in terms of decimal places |
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| place value number system |
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| the value of a digit depends on its place, or position, in the number. Each position is related to the number next by a common ratio. (from right to left) What ever # is in the 2nd column is the first # squared, the thrid is the first # cubed and so on |
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| a number system is a set of numbers |
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Babylonian number system is base 60. Each triangle wedge meant 1 so two together depending on the
column it would be counting 60's or 60 squared's. The boomerang thingys stand for 10 |
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also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes.
There are two beads on each rod in the upper deck and five beads each in the bottom for both decimal and hexadecimal computation.
The beads are counted by moving them up or down towards the beam. If you move them toward the beam, you count their value
high speed faster than computer or calcluator
dates to the 14th century AD. And is considered by some to be more accurate than calculators in terms of typing mistakes and it works to preserved...
top beads count- 5, 50, 500
bottom beads count- 10, 100, 1000 |
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Japanese version of abacus
4 plus 1 bead per decimal place |
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The Yuki are a Native American tribe from the zone of Round Valley, in what today is part of the territory of Mendocino County, Northern California.
The Yuki people had a quaternary (base 8) counting system, based on counting the spaces between the fingers, rather than the fingers themselves |
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The Inca (or Inka) civilization florished between 1400 and 1560 . There were 3-5 million ppl in Incan Society. The civilization occupied all of Peru and areas of ecuador, bolivia, Chile and argentina on the south western border of south america.
n important Inca technology was the Quipu, which were assemblages of knotted strings used to record information, the exact nature of which is no longer known.
base 10 |
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| society started florishing around 2000 BCE and used wedges or "cunieform (which means corner) in their number system. The society flourished in Mesopotamia, the area now known as Bagdad, Iraq. There was a pd where there they did use tablets for writing and then suddenly they cropped up again. |
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| The original creators and users of the base 10 system...the europeans took their number system and thus western societies use it |
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| Roman Numerals ad did not have a place value system |
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For the Tshokwe, the ability to draw graphs is apat of their story telling traditions. The Sona are only drawn by men who use their flexible fingers, storytelling ability and drawing skill to weave suspenseful tales
They live in the west and central Bantu area and the Lunda Sud and Norte areas in Africa |
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create decorative art and embroidery and use graphs to decorate homes. The ability to create graphs is political and brings power and prestige
They live in Kuba Capital which is Zaire |
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The knowledge of drawing graphs is related to several myths and rituals that are important to the Malekulan culture. The Nitus graph is important to learn during life because it is the graph that one must draw to get into the land of the dead. The style is to repeat the same design/procedure over and over again
They Live on Malekula Island which is one of the Vantuatu Islands |
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| micronesian ppl of the Gilbert islands( they speak gilbertese) |
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| The point where two or more lines meet. The amount of degrees in a vertex is counted by (pretending place one's self at the intersection of the edges (vertex) and figuring out how many different paths you can take if you were walking along the lines) |
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| Leonard Euler's proof-> is path in a graph which visits each edge exactly once. Similarly, an Eulerian circuit is an Eulerian path which starts and ends on the same vertex. |
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| conditions of eulerian path |
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There are two ways to discern if a planar graph is Eulerian upon looking at it:
1st) all vertices must be of an even degree...
2nd) there can only be two odd vertices and the rest even
This is because (when drawing a graph w/o lifting the pen or retracing a line) there has be an even amount of ways to enter into a vertex. The way to go in and come out come in pairs in a eulerian path. |
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| A continuous and closed curve that does not cross itself. It always divides the plane into an inside and outside |
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(greek term for "Same Shape"
isomorphic structures are structurally identical. This means that the amount of vertices and edges can be placed in a one to one correspondence.
Also two graphs are isomorphic when u can tell the same story about them both |
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| vertical versus horizontal |
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| number words in african cult |
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| connections between number words show that there was a common lnaguage at some point, trade, war |
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| counting on finger or what not...the zulu use lfet hand palm up pimky cross over to thumb |
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multiplication consisted of doubling
Did not have base system
1- tally
10- upside down u
100- 9 looking thing
1000- crescent moon, line, and hourglass |
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| numerator only in terms of one |
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| kou-ku, pythagorus thoerm |
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| The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c). ....leg^2 + Thigh^2= string pulled tight ^2 |
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| Jordan Curve Theorem (discerning if it's inside) |
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| If you have to cross a boundary an odd number of times to get to the x then it's inside |
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| Jordan Curve Theorem (discerning if it's outside) |
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| If you have to cross the boundary to get to the x an even number of times it's outside |
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Bilateral symmetries- if both side are identical vertically
Rotational symmetries- if you rotate it a certain # of degrees it'll look the same
Reflective is NOT a symmetry because you are essentially creating a completely different object |
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Positive # are closed under multiplication and negative numbers are not closed.
Closed is when the answer you get after doing a |
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= to (probability of the event) X (value of payoff) + (probability of event ) X (value of payoff) repeated
average exp. value in dish = (all the outcome in dish) (1/64 x .5) + (1/64 x .1) ect |
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| Prob of event= # of equally likely outccomes of an event u r calculating / total possible # of equally outcome |
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factorials ( N!)
u r counting every separate arrangements SO YOU CARE ABOUT THE ORDER THEY ARE IN |
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Combinations
6 choose 3
6 sets of 3 |
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YOU DONT CARE ABOUT ABOUT ORDER b/c u r just choosing and would like to know How many sets can be made up of the objects.
NO repeats so u make up for it
4 choose 3
4. 3. 2/ 3.2.1 |
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| REFLECT UPON THE FOLLOWING ITEMS- have examples- specific evidence------------------- A) all cultures have mathematics B) math of a given culture solves probles this culture wanted to solve C) how do pep know about the math of the time |
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| If i had to teach a math, how would i use some alternative methid to make more intersting , taken form some of the cultures talked about |
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| geometric representations , oral history, drawingin sand, names in islam |
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| using geometric methods from islamic sources show how to solve a quadratic equation with a positive solution |
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| compare and contrast the types of proofs seen in specific cultures- Chinese, GREECE (Ko-kou, square root of 2) link the method of proof to which culture it came |
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| Review the analysis of the game dish. Be able to calculate the numbers of distinct ways to get a part number of black or neutral, the total numbers of possible outcomes, usingthe multiplication principle, review definitionof the probablitly of an event. recall the probabiltiy of an event |
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| be able to reconsturct the mera presatara |
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| use the meraperstrara to detrermine the nmerical values of n choose k and raise bonomials t powerrs |
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| be able to explain why 6 choose 3 equals 5 choose 2 + 5 choose 3 |
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| Explain the problems Hindu culture that made the erapestra of interest. What did jews us combinatorics use for"? |
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| poetry needing to have every combinaation, chandra sutra- |
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| Review triangles and the pythagreum thero ---A) be able to explain how to use the tangent function, using islamic methods, to find a triangle B) be able to soleve tow problems using kou-ko (lily pond, somthing else) C) be able to draw a figure to work out soe algebraic idenity such as (x+4)2=x2=8x=16 |
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| Review the definition of group and think about how you might show something is group ( like say rotations of the hexagon) |
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