Alex+Dennis

**April 15, 2011**

 * 1.** René Descartes has made many contributions to the field of mathematics. He is responsible for the creation of analytical geometry, or better known as Cartesian Geometry. He also used math to solve scientific and medical problems. He tried to spread the idea that math could be used to solve every problem in nature. He tried to apply mathematics to the scientific and medical field, and create a standardized method for using mathematics in science.


 * 2.** I believe the most significant contribution of René Descartes to mathematics was his creation of Cartesian Geometry. Cartesian Geometry is a way to use algebra to solve geometric equations, and has a wide range of uses. The uses can be as something as simple as lining up something correctly, or used in the sophisticated engineering and technology of today.


 * 3.** Maria Gaetana Agnesi was a very intellectual woman growing up in a world owned by men. Many intellectual women (other than women in Italy) were looked down upon, and many women could not get an education outside of religious services, such as nunneries and monasteries. She had mastered over 4 languages by the age of nine, and went on to become a very intelligent mathematician. She accomplished all of this with a difficulty to obtain education and the opposition of men.


 * 4.** I found the Midpoint Formula to seem useful in many situations. There are many times in your life when you may need to find the midpoint (or point equidistant from both ends) of a line, without having to guess. It may be very useful for graphs especially. This can be used in many careers and can be used for jobs such as construction, design, carpentry, just to name a few.

Starting from point (0,3), I used the slope (-1/2). Rising -1 and running 2, I found the point (2,2). Since I can use the inverse of the slope to find a point on the other side of the origial (0,3), I started from (0,3) and used the slope (1/-2) to find the point (-2,4). Since it takes 3 points to accurately create a slope line, and it runs through the required point (-2,4), I have completed the equation.
 * 5.** y=(-1/2)x+3

**April 29, 2011**

 * 1.** I would consider Johann Kepler more of a scientist than a mathematician. While he did use math to discover almost all of his work, he did it for the advancement of science. Conic sections helped impact his work with celestial bodies, since planets, starts, and orbits almost always tend to be spherical. Kepler's contributions to mathematics include: Giving first proof of how logarithms, discovering 2 new polyhedra's, working with optics, and many more contributions.


 * 2**. Logarithsm can be used to represent anything that varies exponentially, and also can be used to represent musical scale and how we hear things in the world. Logarithms can be used to describe many physical phenomena in our world. They can be used in place of very large numbers, making calculations more simple.

The function for logarithms is: **g(x) = log**b of **x** where b is the base and x > 0. Some examples of logarithmic functions are: 3^4=81 is 4= **log**3 of **81** 5^2=25 is 2= **log**5 of **25** (1/2)^-4=16 is -4= **log**(1/2) of **16** g(x) is the exponent, b is the base, and x is the solution.
 * 3.** Logarithmic functions were a great source of confusion to me in chapter 8, and also in Algebra 2. I always had trouble deciding which number went where, but now I can do logarithmic functions with considerate ease.

6x-6y=42
 * 4.** 2x-3y=18 =

== 4. Write a consistent, independent system of two equations with two variables that has a solution of (3, - 4). Then solve the system. ==

May 13, 2011
The three famous problems of antiquity are as follows: 1. To trisect and arbitrary angle; 2. To construct the length of the edge of a cube having twice the volume of a given cube; 3. To construct a square having the same area as taht of a given circle. It is interesting to me how the Greeks did not permit the use of rulers and markings for length. The way that they went for abstract art over convenience and reliability shows their devotion to geometry.
 * 1.** The information on the article is about the Greeks thoughts on mathetmatical science. They did not study algebra, they believed geometry was the superior math. They were not allowed to do geometry with any other tools than a compass, to draw arcs and circles, and an unmarked straightedge for drawing line segments. Greeks were not able to accomplish 3 constructions with these tools, therse are known as the //three famous problems of antiquity.//


 * 2.** Squares can be used in construction, such as floor plans and blueprints. Rectangles can also be very useful in this way. Circles and spheres can be used in construction also, but can provide very sturdy objects such as roofs. Triangles can be used to create squares and many other shapes. Cylinder's are often used in construction, engineering, and things such as weapon making.

If I could have a conversation with Euclid, I would ask him "Were you a single man, or were you a team of various mathematicians? Are you solely responsible for your work, or did pupils and people write other works under your name?"
 * 3.** Euclid of Alexandria was vital to the discovery and advancement of mathematics, especially geometry. He is responsible for the work called //The Elements//. Euclid is responsible for many deductive systems for the presentation of mathematics, he solved many arithmetic problems with solid geometry, and also had many other books and works that helped in the advancement of mathematics.


 * 4.** A rhombus is a quadralateral with parallel opposite sides, but all the sides are equal (a=b). A parallelogram is a quadralateral with parallel opposite sides as well, but only the opposide sides and angles are equal.A rhombus has all equal sides, but a parallelogram does not need to have all equal sides. Therefore a rhombus can be a parallelogram, but a parallelogram does not have to be a rhombus.