Lolz (For the record, I'm really a guy like I say in my profile). I wondered if this would happen but I don't remember anything analogous to use in place of the word.

From what I can recollect (its been donkey's years, mind you) my math teacher used to call all the algebraic formulas and methods for making measurements like areas and volumes and such as mensuration. You know, like Hero's formula for the area of the triangle etc.

 

That's hilariously ironic given your avatar.

 

dude that HERONS formula, right? to find the area of triangles using semiperimeter.

 

Well, I support learning about reciprocals instead of division. People would not have to memorize that stupid quotient rule.

 

Yep, but they called it Hero's formula in all the text books. There's one for cyclic quadrilaterals as well.

/derail

 

I always call it the 'triangle thingie'... And it's Heron's formula at least around here...

 

Uh... I don't recall learning the Venn Diagram in math. We always used it as a compare/contrast device for English.

Did my math classes really suck, or did I sleep too much? Or both? >_>

 

tl;dr: Longwinded stuff--an illustration of why anyone would care about Venn diagrams.

A lot depends on the teacher and the style of pedagogy, Red Aviary. Most of the best mathematicians (and physicists, engineers, etc.) tend to be visually oriented thinkers and Venn diagrams offer an elegant visual solution to many problems. The best math teachers (in my opinion) use such means to represent concepts and don't limit themselves to just showing steps without sauce.

For example, suppose I asked for all pairs of integers whose GCD is 121 (11^2) and whose LCM is 1480556 (which is 23 * 19 * 11^2 * 7 * 2^2). You know one pair off the bat: {121,1480556}, but what about the others? Normally, this would be a pain in the ass to do, but if you know how to represent GCD and LCM using Venn diagrams, it's pretty easy.

GCD and LCM are represented in Venn diagrams in the following way: Make a Venn diagram where each number has its unique factors in its own circle and all the common factors in the overlap. The GCD of two numbers is the product of numbers in the overlap. The LCM of two numbers is the product of the unique factors on both sides of the diagram with the numbers in the overlap.

Start by making a Venn diagram with the GCD factors in the overlap and all the other factors on the left hand side:

( 23, 19, 7, 2 ( 11, 11 ) [nothing] )

This Venn diagram represents the pair of numbers, {1480556, 121}. Here the "( ... )" refers to a circle in the diagram. The "( 11, 11 )" is the central overlap region. The "(23, 19, 7, 2^2 (" is the stuff exclusively in the left circle and not in the right. The ") [nothing] )" is the stuff (nothing, in this case) exclusively in the right circle and not the left. Now move each group of prime numbers on the left to the right, one by one. You get the following sequence of Venn diagrams:

The first is:

( 23, 19, 7 ( 11, 11 ) 2^2 ) -> {3059, 484}

3059 = 23 * 19 * 7 * 11^2 and 484 = 11^2 * 2^2. Do the same with all the others:

( 23, 19, 2^2 ( 11, 11 ) 7 ) -> {1748, 847}
( 23, 7, 2^2 ( 11, 11 ) 19 ) -> {644, 2299}
( 19, 7, 2^2 ( 11, 11 ) 23 ) -> {532, 2783}

Now move over all pairs of prime factors (and their powers):

(23, 19 ( 11, 11 ) 7, 2^2 ) -> {437, 3388}
(23, 7 ( 11, 11 ) 19, 2^2 ) -> {161, 9196}
(19, 7 ( 11, 11 ) 23, 2^2 ) -> {133, 11132}
(23, 2^2 ( 11, 11 ) 7, 19 ) -> {92, 16093}
(19, 2^2 ( 11, 11 ) 7, 23 ) -> {76, 19481}

And that's it. There are no other pairs. (Moving over groups of 3 numbers repeats the sequence of pairs of numbers obtained from moving over just 1 number; moving over 4 numbers repeats the initial pair from moving over zero numbers). Incidentally, the reason you can't just move over one 2 and not the other is because if you did, then you'd have a 2 on both sides, so the 2 would really belong in the overlap (thus changing the GCD to 2*11*11 = 242).

Using Venn diagrams, you can prove by inspection that the product of the LCM and GCD of any pair of numbers is just the product of that pair of numbers. (Try it and you'll see). Any time in math you can just draw a picture and the answer jumps out at you immediately, it counts as cool in my book.

 

http://knowyourmeme.com/memes/48293 Don't know how accurate this is, but I remember seeing it on someones Facebook wall.

 

Venn Diagrams can also be used in set theory and probability. A simple example problem:

In a group of 38 students, 21 students like to drink Ginger Ale and 23 students like to drink Coke. 4 students don't like drinking either. How many students like to drink both Ginger Ale and Coke?

Also, if you ever have the chance to take discrete math, do so. Modular arithmetic + GCD/LCM is pretty awesome.

 

Venn Diagrams are a great way to teach elementary set theory, but I suppose they're not absolutely necessary to do so.

 

WELL I GOT A QUESTION FO U SMAARTY PANS WHATS DA SQARE ROOT O YA MAMA>!>!>!?!?!?!?!?!???!?!!!?!?!?!?!QUESTIONMARK?!?!?!?!?!!!?!!?!?!?11111ONE1!!!!11121/

 

/fillerfiller