Kalyn+Hill

5/13/11
=== 1. In the article dealing with constructions, it talks about the different types of basic constructions such as construction a perpendicular bisector and copying an angle. The greeks thought that constructions needed abstract beauty and any application resulting in their work was nice but was not really important to them. They had rules about constructions and they were only allowed to use a compass and a straightedge. The straightedge was to have no markings on it so you could not measure with it. The three problems of antiquity are to trisect an arbitrary angle; to construct the length of the edge of a cube having twice the volume of a given cube; and to construct a square having the same area as that of a given circle. The points of interest to me are the different ways to construct things and the history they give about it. ===

Octogon - You can find this shape on every roadway as a stop sign.
=== 3. Euclid is nicknames "The Father of Geometry", he wrote the book Elements and contributed things such as Euclidean geoometry, numbery theory, conic sections, spherical geometry, and many other books. They are important to math today because they helped in the advancement of many math topics and answer a lot of questions. If I could talk to him I would ask him about his family and what sparked his interest into studying math. ===

===﻿1. He contributed to or created: the law of reflection, cartesian geometry, descartes rule of signs, analyitic geometry, law of conservation of momentum, principles of philosophy, and infintismal calculus. === ===2. I think that the most important thing he contributed was Descartes Rule of Signs. It is the most popular of things he created and it is used in many math practices today. === ===3. Something I found about Maria Gaetana Agnesi was that she was the oldest of 21 children and had to teach all of them for school. She never went to school and knew all about math herself. === ===4. I think that the distance fomula was most useful from section 8-1. D= The square root of (x2-x1)+(y2-y1) to the second power. When using the coordinates (-3,5) & (6,4) you plug in the numbers and end up with the answer of the square root of 82.===

4/29/11
====1. I think that Johann Kepler is more of a scientist than a mathematician because most of the work he did even though math related was for astronomy. He used math techniques to help further him in that but his primary study was not math. He discovered some math conjectures and a law but they both pertained to the advancement of astronomy. He used the conic section ellipses to help explain how plnets moved around the solar system. The ellipse impacted his work greatly because it changed another thing that people knew aboutour solar system. He contributed Kepler's Law of Planetary Motion, Kepler's Conjecture, Mysterium Cosmographicum, and Astronomiac Pars Optica. They are still important today because they are the base of a lot of astrological research and findings. ==== ==== 2. Three ways you can use logarithms are financial growth and decay, finding pH, and measuring the decibals of sound. ==== ==== 3. A type of problem that gave me trouble initially are the system of equations with three equations. I had no idea how to eliminate all of the variables but Inow understand how to do so. The solution to these types of problems are that you have to pick two equations two different times and really use your knowledge of elimination and/or substitution. You then use the eliminated variable and plug it into one of your equations you found using the two equations and then pluggging both variables into the original equation. It works every time! ==== ==== 4. I used elimination and I used to two equations x+y= -1 and 2x-y=10. I solved it and it came out with the solution (3,-4) ==== ==== 5. I would explain it by saying it is exactly like regular equations with equal signs. The only times you have to worry about the equal signs is when you are graphing and if you need to switch the sign around. I would show them that the or equal to in the sign means its a solid line and how to test a point to know which way to graph. ====