Fractal Geometry is a somewhat new branch of mathematics that was developed in 1980 by Benoit B. Mandelbrot, a research mathematician in I.B.M.'s Thomas Day Watson laboratory in New York. Mandelbrot was experimenting with the theories of Gaston Julia, a French mathematician when he discovered the fractal set was discovered. Julia dedicated his life to the study of the iteration of polynomials and rational functions. Around the 1920s, Julia published a

Atheist In "On Being an Atheist," H.J. McCloskey discusses what it means to him to be an atheist. In doing so, he criticizes the classical argument in favor of God's existence. This is not a new criticism, as people have been arguing about whether it is possible to prove or disprove the existence of God for years. However, McCloskey goes further in his argument against the existence of God by

Note the distinct similarities. An examination of Escher's Circle Limit III can thus tell us much about distance in hyperbolic geometry. In both Escher's woodcut and the Poincare disk, the images showcased appear smaller as one's eye moves toward the edge of the circle. However, this is an illusion created by our traditional, Euclidean perceptions. Because of the way that distance is measured in a hyperbolic space, all of the

For instance, classical mathematicians by definition rely on Plato's theory of forms as the underlying basis of their mathematical worldview. The Platonist assumes the existence of true, immutable, and universal forms and structures that the mathematician approaches through the language of numbers and equations. For instance, the classical mathematician holds to the Platonic belief in the expansion of pi; to approach the expansion of pi from any other perspective

relearn several mathematical concepts and learn how to instruct other about them. It also became necessary to learn the different components of educating students on math based upon their current knowledge and abilities and how the teacher will evaluate the students to make that determination. Not only did I learn how to teach the subject, but I was also instructed on how to submit and fulfill standards. In short,

Empiricism Whenever a person chooses a side in the traditional debate between rationalism and empiricism, that person is necessarily making a statement about how much people should trust the evidence of their own senses. However, there are a number of instances in which I think that sensory evidence can be deceptive. While I think the allure of empiricism is undoubtedly seductive, for the precise reason that sensory experience can be so