Jon's Goals

During this summer Academy I feel like I have gotten better at math and learned how to do geometry. I feel like I have gotten better at paying attention to the teacher and learning to do the assignments. For the future I don't really know what I want to do. Hopefully during high school I know what I want to do and figure out what college will help me achieve my goal.

Jon's Country of Math

The Ancient Aztec Calender has many different designs to tell the month, the day, and the year. The top rectangular shaped elemnets represent 13Acatl orThirteen Reed. They say that it represents the date upon which the Aztec Calender was made. They started to times all the numbers that represent the shapes together. 4 x 29 x 49 x 8 x 26 = 665600 after they got that number they used the Maya Companion number to get the number 1366560. The one thing that remains to be computed is the 13 Acatl number but someone would already visualize the symbolic math of the 1366560 day count number on the Aztec Calender.

Jon's Centroid Triangle

The centroid triangle we made was able to balance on the median and centroid. We had to put the pencil to aline with the midpoint, median, and vertex. The reason why the triangle balances on the pencil is because of the center of gravity. The length of the shorter segment is 2 times smalller than the longer segment. We need the proportion to help find how many times does the shorter part of the median fits into the longer part of the median.

Jon's Fibonacci Numbers

The appears in many proportion of famous Greek temples.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#art
The plans for the college are based on the fibonacci numbers and several geometric diagrams.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#art
The cows are a adapted way of Fibonacci's rabbit but making the problem more realistic in the way we observed them.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#dudeneyscows

The fibonacci numbers are a sequence where the firswt two terms are both 1. Subsequent terms are generated by finding the sum of the 2 previous terms. The sequence is 1, 1, 2, 3, 5, ... N is the number of term and F(n) is the value of that term. Proportion is two ratios that are equal to each other. The quadratic formula is the formula to determine the root of a quadratic equation from its coefficient. To figure out the equal of the proportion you need to cross multiply to figure out the answer. The golden ratio is used to find the proportion of height to width when laying out test or illustrations.

Jon's Numbers

Here is the picture of the Numbers activity I did, that shows the patterns of the victims. The pattern forms a triangle and a circle. The point of origin is in the middle of both the triangle and circle. The vertices are the victims and the circumcenter is the point in the middle of the traingle that is intersected by the perpendicular bisectors. I used the computer's geometry sketchpad to construct this picture of the circle and triangle of the victims.

Jon's Geometric Art

Here is a picture of the astrid I made on the first day of geometry class. I had to use a ruler and graph paper to connect all the lines to form the line of the astrids. It has a reflectional, rotational symmetry, and line of symmetry on the picture.

Jonathan Tetrahedron

Here is my cool looking picture of my Tetrahedron I made with my cool friend Janet. The circumcenter is in the middle of the Tetrahedron where the 3 small straws connect to each other. We made a Polyhedra for one of our class assignments . There are 3 regular traingles in the tetrahedron to make it. All the angels are equilangular when having a regular triangles and its also equilateral. The sides of the straws are concurrent to each other. The centroid is also the same as the orthocenter of the tetrahedron. The orthocenter is where the three middle size straws is at in the Tetrahedron.

Airplane

Here is a picture of my cool looking airplane. I would change my airplane so that it can actually fly instead of being just for show. I would like to win the Longest Distance contest and make my computer more simpler so that it can fly better.

Jonathan Reflection Image

Here is a picture of a polygon I chose with Ted in class.

Here is a image of a reflectional image of a O.