My Fruity Goal Blog

What I improved on during this Geometry Summer Academy at Oakland High, is doing my home work. I really didn't do my home work a few days in a row, but I improved my home work habits. My ultimate goal is improve my study habits.

Fruity Mathematics used by Ancient Muslims

In this paragraph I'll be talking about how the ancient life of Muslims used mathematics, especially trigonometry.


Trigonometry is also mostly a Muslim creation. It is a branch of mathematics which studies plane and spherical triangles. It developed from the need of astronomers to map points in the sky on a heavenly sphere. Trigonometry's functions, involving ratios such as sine and cosine, tangent and cotangent, were greatly developed and refined in the Islamic lands.



Arab contributions:

Al-Tusi, a Muslim, is the "father of trigonometry".
The idea of trigonometry was originally from the Greeks, by Hipparchus in 140 BCE.
The Muslims further developed trigonometry from their work in astronomy.
Today astronomers use trigonometry for calculating distances to stars, and for measuring distances and heights of buildings, trees, etc.


Top: Western Arabic or Hindu-Arabic Numerals

Below: Modern Arabic numerals which developed from them

[ Still Under Construction ]

Jenea's Fruity Paragraph About 3.5 Centroid Steps 9-11

Here is another real life example of a centroid triangle I made with Jonathan. This second picture of the centroid triangle, we used a wooden pencil to balance the triangle vertically.

Here are real life examples of a centroid triangle I made with one of my friends Jonathan. The first picture of the centroid Jonathan and I made, we used a regular wooden pencil to balance the triangle horizontally.

[Still Under Constrcution)

Jenea's Fruity Paragraph About Fibonacci Numbers

In this paragraph, I'll be talking about how Fibonacci Numbers relate in nature and reality. There are very many similarities between Fibonacci numbers and different types of living plants, fruits and animals. Mathematicians are very inspired by the Fibonacci quadratic formulas, especially the Golden Ratio.


This is a real life picture example of a fruity fruit called a pineapple. As you can see the pineapple has proportions.The number of turns in the spiral (from leaf to leaf) and the number of leaves that exist in the pattern in all cases express a Fibonacci fraction and therefore a Fibonacci ratio. The same pattern repeats over and over as the plant grows up. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space. So nature isn't trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why the spirals are imperfect. The plant is responding to physical constraints, not to a mathematical rule.


This is a real life picture example of a flower, it forms a Fibonacci Sprial.


The Following Links I Used:


[ Still Under Construction ]

Jenea's Fruity Paragraph About Numb3rs

This is a paragraph about the show/episode my whole class watched on July 16, 2007 called Numb3rs. The show called Numb3rs is about a man named Rob Morrow, who works for the police in the investigation department as an FBI Agent. He's trying to find out who the L.A rapist is, the person who's been commiting crimes in Los Angeles. Rob Morrow has trouble on finding out where the perpetraitor's home is or where he works, even by using the computer he still can't construct a a motive or alliby. His gifted brother, Charlie Morrow helps him and the Bureau on finding out where the suspect is by using "Numb3rs" to find out the point of origin where the hot spots are or where the rapist is hiding at. Charlie used the map to find the area where the victims were raped and killed. By using the map grid he made calculations to make probablilities that formed a triangle shape, then he made a perpendicular bisector of the triangular shape to find where the suspect might be, by finding the circumcenter of the triangular shape. Charlie pin-pointed where the perpetraitor lived, but he never thought of where the perpetraitor might work untill his older brother Rob gave him the idea. So Charlie found a second point of origin or hot spot where the suspect worked.

-Jenea Bilateral =]

Jenea's One Fruity Colored Tetrahedron

This is a picture of my groups tetrahedron. I worked with my friends Alex, Victoria, and Khanh on making this polyhedron. The materials we used to make our tetrahedron, were yarn (green), straws (clear), and a regular needle. The tetrahedron we made makes a "Regualr" or "Equilateral/Equilangular" triangle. The tetrahedron we made looks as if there are equilateral 3D triangles in more 3D equilangular triangles. In the regular triangle you can see the circumcenter, the incenter, the orthocenter, and the centroid in the figure. If you see it in the inverse position then you can see the exact same thing. I seems as if it has rotational symmetry in it.

Jenea's Fruity Daisy Design c;

This is a picture of my "Fruity Daisy Design." I created this picture with a ordinary compass on a peice of binder paper. The picture has reflectional symmetry, rotational symmetry, and line of symmetry. As you may already see in the picture, the daisy has a pattern to it. I colored the daisy with light pink color, and a type of violet color also in a pattern like form.

Jenea's Fruity Colored Airplane C;

I entered my airplane in the following contests:

The Furthest Paper Airplane Contest - Lost *So sad*
The Straightest Paper Airplane Contest - Lost *So Sad*
The Fanciest Paper Airplane Contest - Lost *So Sad*
The Farthest Paper Airplane Contest - Lost *So Close*

If there ever was going to be a next time to enter any of the contests above then I'd want to create a(n) airplane to fly the fanciest.

Jenea's Hexagon and Reflectional Symmetry

Here's a(n) picture example of the leaf that I found in search of reflectional symmetry. This leaf is an example of reflectional symmetry. Down the middle of the leaf you can see the reflectional symmetry.

Here's a(n) picture example of a beautiful white flower that I found in search of a hexagonal shape. This flower is an example of a hexagon. The petals that are on the flower make a hexagonal shape.