Wolfram Alpha

As our year continues and the concepts we delve into get more and more complicated, sometimes classroom learning and textbook learning isn't enough. One method I have personally used this year is checking my work using an online software development that makes all systematic knowledge immediately computable by anyone. This website is called Wolfram Alpha and I have found it incredibly useful in my studies this year. I have found it particularly useful in checking my work on difficult problems since it provides step by step instructions on how the problem is solved. One of the things I really like about this site is the graphing capabilities it has. You simply type in the function and it will give you a picture of the graph, the integer solution, the domain, range, the derivative, and even allows you to interact with the graph to manipulate it. Another interesting feature of this site is it's random feature. You simply click the button and it takes you to a random problem. This is interesting because you can learn about all sorts of different math problems and how they are done with relative ease.

One thing I have learned is that you cannot simply rely on this site to do everything for you. Like many things, nothing beats instruction from a knowledgeable instructor where you can ask questions and interact in real time. I have found that this is best used as review and checking your work rather than relying on this site to teach it to you.

Once again here is the link to the site incase you were interested about looking into it further: WolframAlpha.com

Fountain Valley Commencement Speech

This speech by Dr. Stefano Bertozzi is a lesson that anyone can realize the importance of and begin to undertake. The gist of Dr. Bertozzi's speech is to not 'eat more than you bring'. The meaning of this is don't take more from life than you give. While this might seem simple, its a very hard thing to accomplish, especially for privileged students like us who attend the Academy. In our short lives, we have eaten far more than we have brought. So it is up to us in our years after high school to make up that debt, and be more like the teachers who educated us along the way. This reminds me of a quote that my parents drilled into my head from a young age, "Leave things better than you found them". This goes hand in hand with Dr Bertozzi's quote and expresses the same ideals. It should be our job in this world to improve the planet for future generations to come. With serious problems in our world like global warming, racism, and AIDS, we have grave issues that need attention, but if we commit ourselves to the tasks, I feel that our generation can easily bring more the the potluck than we take.

The Wonderful World of Tessellations

I apologize for this being turned in so late. I was looking through my canvas the other day and I saw I didn't have a grade for this blog even though I remembered writing about it. I went to my blog and somehow I made the blog private and saved it in my drafts instead of publishing it. I apparently also forgot to email my link to you. I am so sorry for this being turned in so late! - Seth

For this blog I decided to explore the topic of tessellations.  The earliest time I can remember seeing tessellations was in 6^th grade.  I remember seeing a poster of a sketch by MC Escher. Here is a link to that piece of work: http://brettworks.files.wordpress.com/2012/04/escher_reptiles.jpeg

Anyway, I remember looking at the reptile tessellation in that sketch nearly everyday during my first year at the Academy.  Eventually I became fairly interested in tessellations and did some research of my own into the subject. I found out that there is only three tessellations that are composed of regular polygons that symmetrically tile.  These three shapes are triangles, squares, and hexagons. This is because each of these shapes has interior angles that are divisible by 360 (60, 90, and 120 respectively). Thus, only a shape with an interior angle that is a divisor of 360 can tessellate.  

            

One tessellation of this kind that is seen frequently in nature is the hexagonal tessellation. This is more commonly recognized as the honeycomb. Bees tessellate their hives for many reasons. One of the reasons is because it allows for maximum storage within a small space.

            

However, there are other types of tessellations. There are 8 tessellations that combine two or more regular polygons in the same order each vertex are known as semi-regular tessellations. I have also seen these referred to as Archimedean tessellations. Here is an awesome picture of semi-regular tessellated tile: http://euler.slu.edu/escher/upload/3/30/Semi-regular-Seville.JPG

            

Finally, there are 14 possible combinations for demi-regular tessellations. These are composed of the eight semi-regular and three regular tessellations. One place where this kind of tessellation is prevalent is in Islamic architecture and art. I found this neat picture: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzbsBH5pOmBatDgnq6MJrjCafYEgAs3NFCrG7OgVU8oVu3UGsjZc9z57uWoHvKtfXAkxX-QP7BmD_I_4d7Jv4ZkI9LCUGz9UZXm7RkGaCC2HIgFdQObgcqpGFh1a87Y6vczqajqAPpMyg/s1600/DSC00101.JPG

Blaise Pascal

Pascal was born 1623 in Clermont-Ferrand, France. He was educated by his father who was a tax collector who had a penchant for mathematics. Upon moving to Paris in his early childhood, his father decided to educate Blaise himself. Remarkably, in his initial curriculum, mathematics was omitted. However the young Pascal was now even more interested in the "forbidden fruit" that was mathematics. He studied geometry on his own and even fabricated his own terminology. Eventually, his father allowed him to read the works of Euclid. Pascal learned many things from reading the works of Euclid. This thing would be important when Pascal began to formulate his own theories.  

Some of his inventions include the Pascaline, an early form of the calculator. His primary inspiration for this invention was because of his fathers work as a tax collector. In 1655, Pascal accidentally created a roulette table while trying to create a perpetual motion machine. Pascal's most well known invention is his triangle. His triangle is truly a creation of beauty that has significance far beyond the realm of mathematics.

Math Humor

Why is Xbox 360s successor called the Xbox One instead of the Xbox 720?

Cos 720 is 1.



Home on the Range:


Why is it dangerous to multiply by the complex conjugate?

Because someone could lose an i.






Why did the Klein bottle have no friends?

Because it was so full of itself.