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Venn Diagrams and Sets
Transcript of Venn Diagrams and Sets
Dun dun dun ! Set Language This section shows where sets and venn diagrams
are used in daily, normal, not so mathmatical life :) Where are
they used ? We will explain the history of all the topics we have mentioned. Don'y worry, it won't be boring ! History By Luke Collister, Sam Morelius
and Jamie Mason THE BASICS What are Venn Diagrams ? What is a Set ? We have prepared a small quiz. Some of you will be chosen to answer questions. Good Luck ! QUIZ used to show They are the different relations between different sets. They are basically squares with circles in them. These circles repres- ent sets, where one circle represents one set. Where the sets overlap each other is the relation between those two sets. If this isn't a clear explanation of what a Venn Diagram is, we will show you a "very complex" AN EXAMPLE ... diagram in a minute. This should help you understand them. SET LANGUAGE "Union" If A U B is written, this means everything in A AND B. U "Intersection" If A B is written, this means the section that includes A AND B. "Not" If (A' B U C) is written, this means the union of B AND C, but NOT A. ' "Not equal" If (A ø B) is written, this means that A is not the same as B. ø A set is a coll- ection of ob- jects called ele- ments which are cl- early defined. Sets can be shown in venn diagrams. Check out this example to see QUIZ The person on "Who Wants to be a Millionaire ?" today is ... JAIME ! ANGEL ! LOL JOKE ! It's really ... Whoever is the best listener will get to take part in the quiz. There is a prize for whoever reaches $1 million as well ! OPEN POWERPOINT QUIZ ... How are Venn Diagrams used in a non-mathematical life? Well, we are now pretty much familiar with Venn Diagrams in Mathematics, but they can even be used to express things in any day life. We will look at how they are used and why. We will look mostly at how the media uses Venn Diagrams using the help of Google and Wikipedia. In an exclusive interview held over the internet, they "told" us that the media uses Venn Diagrams on a daily basis, but also how Venn Diagrams are used in other places you might not expect, like a dating website. Venn Diagrams start relationships ! OMG ! What is the world coming to ? Well, the weather department or whatever its called, use Venn Diagrams. They collect data from satellites and weather stations and put them into appropriate Venn Diagrams so it is easier for the forecasters to read the information that has been recorded. They don't show the information that has been recorded on television in Venn Diagrams, because it would take everyone at least 1 hour to check the weather, and it probably would have changed by then. How does the media use Venn Diagrams? Introduction How are Venn diagrams used to start relationships? Well, Venn Diagrams are used on dating websites to make matches for people. They put your information in one set, and somebody else's information in another set, and where they overlap, is the relation, which means that you have a match. The reason they don't show the Venn Diagram to you is because it is easier for you to understand if they just tell you what you and your match have in common. But to get that information to you, they use Venn Diagrams. Maths starts relationships ! What ? History Venn Diagrams ... what we mean. "Subsets" If (A B) is written, this means that everything in A is also in B. Venn Diagrams were invented by a man called John Venn in 1880. No real surprise why it is called a Venn Diagram At first, he didn´t refer to them as Venn Diagrams, but "Eulrian Circles". Scientists believe that the concept of Venn Diagrams
had originated and had been seen before. However, because he comprehensively surveyed
and formalized their usage. As well as was the the first to generalize them, so whenever Venn Diagrams are discussed within a group of scientists, they are associated with John Venn. In the 20th Century, Venn diagrams were further developed. In 1963, a guy called Henderson showed that the excistance of an n-Venn diagram with n-fold rotationl summetry that impled that n is a prime. He also showed that such summetric Venn Diagrams exist when n is 5 or 7 In 2002, a guy called Peter Hamburger found summetric Venn Diagrams when n was equal to 11 And, in 2003, Griggs, Killian and Savage showed that symmetric Venn diagrams exist for all other primes. Although, symmetric Venn diagrams only exist if n is a prime Venn Diagrams and another type of diagrams called Euler Diagrams were incorporated as a part instrution in Set Theory in the 1960s. This was part of the new math movement, but, since then, they have been used by other curriculum fields such as reading Venn Diagrams correspond to the Truth Tables in the sense that each set, or region of a Venn Diagram corresponds to one row of the Truth Tables. John Venn Here is a picture of the inventor himself, even though he wasn't the first person to come up with the concept of Venn Diagrams, John Venn. In my opinion, he doesn't really look like a super geek in this portrait. The First Venn Diagram ever! According to "top secret" resources, this was the first Venn Diagram that John Venn made in 1880. I can see why this would be his first. Venn Diagrams are
also used ... 1. To categorize data and to put data into different groups.
2. To compare and contrast different types of data or items.
3. They can be used to describe property ownership concepts.
There are many more uses, but we don't have time to list them all !