Monday, September 28, 2015

Time to Net

-Photo Credit 
Nets are things that seem easy once you have the shape and just have to cut out and tape together but have you tried making your own, things get a little trickier. In class we made our own nets for a cube that had three different size pieces. The picture that follows is just one of many ways to make this shape.
-Photo Credit 

In my group we created three different nets that made the same end product. Which just illustrates that there are many different variations of how to draw net next for the same shape. I believe our professor wanted to see how many ways we could visualize the net because the one example was keep up at the front and we were to make the net with only looking at the shapes. This made the task harder and more of a challenge because we were using our imagination to make the shapes which didn't always work but in the end made what our nets all vary in ways.  
As our professor illustrated  its a good thing that in math there are many different ways to come to the final solution and nets are the same. So what are some strategies in finding nets? 
  • How I make them is starting with the the solid shape in front of you and trace that side that is on the paper. Following that you roll the shape across the paper and every time a face is flat on the paper trace it and only do ever face once. This will give you the shape as if you flattened it, then all that is needed is to add tab areas and you will have a working net. 
    • This can and will give many different net because you don't have to roll it the same way every time you start a net. An example of this is net number two below you can tell this because you can roll the shape up and makes the final cube. 
  • Some people just can just look at the 3D shape and see it flattened on a piece of paper. 
    • This will give the base as the center of your net and that makes it easier to build the shape.Most visualized nets will resemble net number one because you can see the sides are wings and the center makes up a four sided box.  
-Photo Credit

These are the most common ways to make geometric nets without the use of technology. But since we are mathematician we like to think about how to optimize these nets and how can we find ways to make it easier, we are lazy and like using our technology. In my resent research I have found many web sites that will help and make shapes that you want nets for. Wolfram alpha has a nice set up for making 2D nets into 3D objects. But then there is always the math major's favorites of Geogbra, Sketch pad, and many other online resources. 
I think that this is a very interesting topic that isn't covered very well in schools. I think that being able to take 3D shapes and turn them into 2D shapes and vise verse are very important ideas to help with students learning and understanding of geometry. It gives students hands on knowledge of how to make and build what they are have been learning about. I know that even in college I enjoyed the challenge of how to build what I saw in front of me. I think this activity is a good active that is needed more in schools because classrooms focus more on the abstract instead of hands on learning once students get into higher level math classes which is sad because there are many activities that can be done in high school math classes.   

Thursday, September 10, 2015

Diophantus's Riddle

This is Diophantus's riddle it wants you to solve to find out how old Diophantus is when he dies. This riddle is somethings that many people don't want to work on because it has the awful fraction that everyone hates but as you work through it the fraction all start to work out and work together. Once you work through it you come to a whole final number. The following is my work on solving this problem.

If D equals Diophantus's age and S is the age of his son you will get the following expressions:

These numbers come from the riddle:
 is how long he spends as a boy
 is his life with a bread
 his life before marriage 
5 years married without child 
4 years after his son died till he died

Now doing the parenthesis first:
Find the common denominator witch is 84 we get 
(33/84) D+S+9
Replace S with (1/2)D and since we know that (42/84) is the same as (1/2) we can replace that as well
Move that D's to the same side,
Even though it isn't asked for we can now find the son's age by using 84 in our equation for S.

So taking what we have just gone through it's time to make our own and since we are all math nerds I will use "messier" fractions. I will being doing this in steps, stick with the steps. 

Step 1: Pick proportion.

   I found what their common denominator is.
Step 2: Variables and additional data.

Step 3:Write the problem
   You're going shopping with your friends and you find your favorite band is selling concert tickets for 1//8 your total bank balance. Continuing shopping you find the best outfit and shoes for the concert which cost 1/15 and 1/20 respectively of you balance. Once you get home you look and see that you have 18/30 of what you started with plus the $10 you have left from lunch. How much did your bank balance start at?

Step 4: Check!
1/8-concert tickets
S-how much left 
10-your change
Common denominator.
Plug in S.
Common denominator.
Multiply the reciprocal of (20/120) to both sides.
That is the final step and since we found a real answer that makes sense with the question asked we have a successful problem to make it more we could always ask:
   How much were the tickets?
   How much was the outfit?
   How much were the shoes?
This is how I worked through the Diophantus's riddle but there are many different ways to do it. Whats your's?
   This problem makes me wonder what else can be shown to students in better ways. This problem is a very good way of showing how fraction can work and correspond to problems that are strictly fraction heavy. I know that during high school I like many other hated fractions and this type of problem I think would help student make a connection to fraction. We all know that once students have a connection to what they are learning then they will not only learn it easier but have a better chance of remembering what they have learned.  

Wednesday, September 2, 2015

5 milestones of Math

What is math? This is a question that has been asked, you would think that being at the end of our math degrees we would have an answer to this but it is the most difficult question. So through this class and this blog I will be creating/thinking/learning what I believe the answer to this question is.
In the history of math there has been many major discoveries, but what are some of the main most important ones. I believe an important one would be discovery of infinity. This was a hard topic for many people to understand and even accept but is the most well known today. I think that without it there would be a completely different math world out there.
Throughout my college career I had to take Euclidean Geometry, which was unlike any other math class I have taken because it makes you think about things you can't automatically see or understand. The idea that there are more then just what we know as Geometry was a wide awakening to me. Which bring me to thinking that this is another major discovery in math of Euclidean.
We would have gotten no where in math without the basic operations of adding and subtraction. To me this was the very beginning of people learning and putting words with what they are doing. There are so many area of life that use these ideas and it to me would be the first and most important discovery.  
  Leading off of adding and subtracting I believe that multiplication and division would also be very important in our math history. Yes it is built of adding and subtracting but being able to use these idea really made math a more universal tool. 
Finally I think that in math when it comes to milestones that we need to know how to communicate what we know to others outside the math world. I believe that over the years we have become better and continue to get better at how it is communicated. I believe that milestone to be the opening up of the math word to the normal person.