The home page artwork was done for fun by geometry student Patrick Chow in 1996. It represents the feedback that can come from bringing mathematics to life in the classroom.
The cover was part of a final project in Algebra 2 by Kendra Cunov demonstrating the effect of integrating math and science. The project consisted of 33 panels illustrating human cultural evolution. The entire project is reproduced below.
THE FOLLOWING ARE EXCERPTS FROM STUDENT PRODUCED ESSAYS. THEIR COMPLETE FORM ARE INCLUDED IN THE TEXT.
Geometry
"The Greeks originated the Western thought process with their careful examination of logic and reason...Socrates came up with the concept of universal definitions, and all Greeks were very concerned with verifying the authenticity of their axioms. It was Socrates who said, 'The unexamined life is not worth living.' ...The postulates and theorems generated by Euclid were followed as if they were the word of Zeus. In fact Plato said, 'Let no one destitute of geometry enter my doors.' Archimedes, student of Euclid, was one of the greatest mathematicians of all time. His invention of the integral calculus and his careful study of pi have provided us with the means to understand both the world of the infinite and the seemingly everyday world of circles. However, it was Aristotle who more than any other figure, embodied everything that drove the Greeks in their search for truth. It was Aristotle who first consciously explored the process of syllogisms, a system of logic by which certain propositions are ascertained to be either true or false based on the validity of prior propositions or assumptions. Aristotle spoke for all Greeks when he said that the ultimate form of happiness for humans is a life governed by reason. If Western thought can be defined as an effort to understand the rationality of the universe through reason, Eastern thought can be defined as anything but. The main difference between these two schools of thought lies in their consideration of paradox..." A.G. '96
"I think the book (Sphereland) was trying to give us some conception of the existence of a 4th. dimension, by showing how 2dimension people conceive of the existence of a 3rd.dimension. The visit to Lineland is analogous to our visiting flatland. This shows us the limits of our comprehension by showing us the limits of theirs. Because the square could see the curve of Lineland, he could imagine his world curving...In the same way the square could see the Lineland expanding into a perpendicular dimension and so imagine the possibility of his own space expanding into a perpendicular dimension..." M.W. '73
ALGEBRA 2
"Mathematics is a key component of the world we live in today. Without its evolution from the simple addition and subtraction of the earliest tribes, none of the science and technology, or even contemporary lifestyles of people in today's world would be possible The roots of math can be traced back to the first humans who recognized and utilized patterns in the natural order of things, because this primitive version of analysis and synthesis was the birth of inductive and deductive reasoning... According to Michelangelo, science is pure analysis, and art is pure synthesis. If this is true, then math is the incorporation of the two. Analysis (deduction) and synthesis (induction) are the basic ingredients of the function. A function is a generalization of any dependency... Thanks to René Descartes and his Cartesian coordinates (the marriage of algebra and geometry), it is possible to graph these functions. A graph is merely a visual display, or a model of some system that has been analyzed deductively... Until we can truly understand the natural systems we have copied (functions may be crucial in achieving this goal), we may not truly have mastered the art that Michelangelo spoke of." A.M. '93
"...From the time we are born to the day that we die humans are continually using paradigms and functions to operate in the world. Whether it be driving an auto to work or playing baseball, mental representations are always guiding us through life... The vast amount of models in the world is the reason man has such a long childhood...It does not take a baby gazelle over twenty years to learn to run fast from prey and eat grass, those activities are (learned) instinctually; but it does take a kid over 20 years to grow up, have a mature relationship, and receive a collage education. Models can be seen as very complex learned behavior. They have been created by man for several reasons, and play a very important role in today's modern lifestyle, as will be explained. As we know, the universe has a tendency toward entropy (disorder) with pockets of high organization. As highly evolved life forms we are extremely organized...Because we are such highly synergistic beings (sum is greater than the parts) it is logical that we would create more organization (models)... This evolution of paradigms can also be called cultural evolution. In this we stand on the backs of giants to build new theories using previous ones...It comes back to the model, it is not an inherent trait or instinct, it is something that isw taught, from one mind to another, and within the transfer of knowledge synthesis takes place in the mind of the learner and the idea evolves further. ...The correlation between mathematical and scientific models is surprising, how one system in math may perfectly describe an unrelated scientific process... B.G. '94 ...A scientific model is like a spoked wheel. It will have a center with supporting spokes. Any one of the parts will be capable of changing the center or the original idea. The model will not be complete until there are sufficient spokes to support a rim. Then the original center becomes a functional wheel. Just as this wheel can roll forward or backward or just stay in place, a scientific model can also. If it is capable of moving forward it can cause the production of further or new wheels. All these wheels moving forward can become the center on which the larger wheel of scientific knowledge is supported. As the currently accepted atomic model was being developed, the central point or idea was redefined many times... Man uses metaphors in his music to explain and express moods...Whether the music is instrumental or has lyrics is of no consequence, it is still a metaphor for the feelings and moods of man. Mathematics is the innovative metaphor. Man has learned to quantify ideas using numbers and symbols. They explain certain theories and ideas without using words. With mathematics man provides structure to his ideas and order to his metaphors...
