Susan's Goals

For this summer program to be over. I learned many things mostly math that I don't know like geometry. It was hard but i learned it little by little and also the academy let me see many colleges and university campuses. It also let me know what are the requirements for colleges and university and that i know what i have to do to get to my goal that is a career in medical. Also I know which classes i have to take to pass high school and also pass the requirements of the university that i want to go. so this is what i learned in the 1st annual summer algebra academy at oakland high school in the summer of 2007 from June 25 to July 27.

Euclid's Element by Susan L.

Euclid's Elements is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates also called axiom, propositions, and mathematical proofs of the propositions. The 13 books cover Euclidean geometry and the ancient Greek version of elementary number theory. The Elements is the oldest extant axiomatic deductive treatment of mathematics, and has proven instrumental in the development of logic and modern science. Euclid's Elements is the most successful textbook ever written. It was one of the very first works to be printed after the printing press was invented, and is second only to the Bible in number of editions published. It was used as the basic text on geometry throughout the Western world for about 2,000 years. For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students. Not until the 20th century did it cease to be considered something all educated people had read.

Centroid Triangle by Susan

Above you see two pictures of the same triangle. So to begin with, the triangle was made on July 20, 2007 by Jenny T. and Susan L.. To make this triangle we had to first we had to draw is on the patty paper. But draw a large one that can Be fit on the cardboard. When finished on the patty paper, we traced or pierced the points of the vertices and midpoints onto the cardboard and connected them to make a triangle with medians that would be the line that was connected by the midpoint and the opposite vertex. We did this 3 times, after that you would see that there is a spot or point that all the medians intersect and that point would be called the centroid so its also the center of gravity or mass for on first picture you see that we balanced on a pencil. If you want to make sure that the centroid is the center of gravity or mass you can balance it on a pencil like the first picture that shows it or measure the lines that are on the triangle that is split by the centroid point. After the measurements. You then, Make a fraction out of them like of the two lines that are split by the centroid it becomes S1 over L1 since S equals to the short line and the L equals to the long line of the median so you do it, also to the other medians and you will find that they all equal to one half but in different numbers. IT'S EASY TO MAKE A CENTROID TRIANGLE!!

Fibonacci numbers by Susan

The one that has the black background is with lines that show what does it has to do with Fibonacci numbers and that and that it is a swan neck that is curved. So then, the black graphing one explains why the swan's curved neck is somehow using Fibonacci numbers or the Arabic-Hindu number system by Leonardo of Pisa. I got the swan picture from this website: http://www.flickr.com/photos/kaddy/85792192/. Also for the black graphing one i got it from here: http://iluvkids.myweb.uga.edu/Goldenspiral.html

The next picture is the lightening and this picture is from this link: http://iluvkids.myweb.uga.edu/nature.html. Fibonacci also says that the number system that he introduced to Europe will also explain nature in numbers. Or the secret of nature.

After the lightening is the DNA. I got this picture here: http://goldennumber.net/images/dna-b.gif. how is DNA related to Fibonacci numbers? Well the DNA's pattern are kind of repeating and so its similar to the Fibonacci numbers pattern and also, it can be replaced as numbers with the molecules of the DNA. So if you want to know what is the Fibonacci numbers are is the next paragraph.

Fibonacci numbers is a unending sequence of numbers that is the sum of 2 numbers before it. Here is a example: If F(1) = 1 and F(2) = 1 it equals to 1+1=2 and after that you take the solution that would be 2 and the number before it that would be 1 and that equals a problem that is 2+1=3 and so on and the solutions that is beore also equals to the F(n) = value of a term. So n would be any term or number that would be subtituted to F(n). All of this is by a italian mathematician whose name is Leonardo of Pisa that lived approximately from 1170s to 1250s. He was nicknamed as Finoacci and that he was also the person that introduced the Hindu- Arabic number system to Europe by his book called "Liber abaci". To find things like finding perimeter of a house like today and other things we use today are things that are from Arabic-Hindu number system. To solve things and also that the golden ratio is also created by him. If you want to find the golden ratio you have to know the Fibonacci numbers. To get a golden ratio, First we have to find the proportion then cross muiltply it then use another formula that is called the quadratic formula to find the golden ratio.

Num3ers by susan

As you know this movie is called Num3ers and that this movie is about the F.B.I looking for a L.A. serial rape killer, who has killed many womens. So the F.B.I ask a mathmatician named Charlie. They asked him to track down the killer's home by using the patterns of the killer's killing and where the location that the killing of the ladies occured. So when the mathmatician using math to track down the location of the killer's home, he used some what geometry and other math courses that i don't know what is the name and for that he used a circle and inside the circle was where the victims were killed and that the victims became the vertices or points of a something that forms a similiar oval or circle and that the killer's house became the point of origin and also the circumcenter and when Charlie made the circumcenter from the location where the victims were killed. It closed down to a triangle between 3 victims that are very near the killer's home. So then, Charlie used the perpendicular bisectors from the victims place and the midpoints from victims to victims and also when they find out the home place he wasn't there and so the F.B.I. thought Charlie had an error in his calculations in finding the killer's home. But then, they founded new informations and so they give this information to Charlie and he starts over and found where it is. But he had to construct it on the map of the town and so he used his computer since it made the job better and printed on the map and told the F.B.I. his new calculations and the F.B.I. found it before it was too late for another victim to be dead. So then the killer was killed. So this is how the killer was found somewhat like this.

TETRAHEDRON by susan

Our tetrahedron was made in a group of 3 COOL girls on 7/13/07 by Jenny T., Muting C., and Susan L.. For our group to make or construct this, we needed 3 different color yarns, 3 needles, and a lot of straws with different measurements that I don't know what is the measures. So when connecting some straws with the string, it started to form a triangle that was equilateral. When finish when making the triangle, we connected more straws by the strings and got another triangle but it was bigger then the first triangle we made. It was also all equilateral. When we connecting straws that was concurrency things together to make a figure were all equilangular triangles. Also when it was concurrent it was also inverse, because we were making a triangle inside the bigger one that is surrounding it and so this is also a polyhedra and also that its centroid is the same. When connecting them, it kind of different for the triangles because the triangles that are surrounding the small regular one. Inside of my tetrahedron, i see an orthocenter is the same for ALL triangles. The incenter was also the same as orthocenter but then it was blocked by one of the straws that were connecting the small one to the one that is surrounding the small triangle. The circumcenter was also used because it was the incenter and the centroid because it is the tetrahedron's triangles with all equilateral. DOES THE TETRAHEDRON LOOK COMPLICATED TO MAKE BUT IT IS VERY EASY ONCE YOU HAVE THE INSTRUCTIONS AND YOU JUST NEEDS TO FOLLOW IT. SO DON'T THINK THAT LOOK COMPLICATED TO MAKE!!!!

Geometric Art - Daisy Design by susan

My daisy design is a design that makes a daisy in the middle by using a compass. You can see shapes on this design while making a daisy inside the circle, a hexagon, and a star. Also you can find line of symmetry and rotational and reflectional symmetry. However, it had different colors on the leaves of the daisy. the daisy design has 4 line of symmetry.

My airplane

This is my airplane that I made in class and after my class finish making a paper airplane we went out to the balcony to have a contest for 4 different things : straightest, furthest, farthest, and fanciest. I wanted to enter the furthest so i did but i lost since there are other people 's airplane went farther then mines. so next time I would like to make a paper airplane to win the farthest contest.

Susan the shape octagon and rotational symmetry

The picture above this blog is a stop sign that its shape is a octagon and its has 8 sides to it and that it has 4 lines of symmetry. Also its has a reflectional symmetry and rotational symmetry since, if you rotate it you will see the same pattern on it, no matter how much you turn it around. When you wants to see a reflectional of it you can just take a mirror facing it and you see a another one that look alike to the stop sign or the octagon shape of it.