Illinois Junior Academy of Science - Yearbook (Urbana, IL)

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To learn about the symmetric curves I applied both synthetic and analytic geometry. Synthetic or Enchidean geometry involves postulates - basic statements that are accepted without proof - and theorems - logically reasoned statements based from previously accepted or proved postu- lates or theorems. This geometry's fundamental tools are points, lines and planes. Analytic geometry primarily uses algebra. Applying both I am now able to reason the answers to a practical problem involving conics. For my demonstration and booklet I drew diagrams showing how conics can be formed by a straight cut in a cone as well as diagrams of conics drawn from an algebraic expression on a coordinate plane. By using cones that I molded from rock hard water putty and then cut and sanded, I proved three-dimensionally that a conic is a plane section of a cone. Because of their properties conics can only be drawn by special apparatuses, one of which I partly developed and built. This was the only working part of my research project.

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letting 1!32 of an inch be one day. The distance between the moire' fringes was 7 15132 inches. So by my calculations a central eclipse occurs approximately once every 239 days. Some central eclipses occur when the angular diameter of the moon is less than that of the sun's so a ring of the sun, the annulus, appears around the new moon. I also drew a third transparency using the same scale to differeniate be- tween annular and total eclipses. JIM RYAN My original problem was to show the use of number systems in a simplified form. I had to extend my knowledge through research. I then went to work on designing an eye- catching display. After trying a number of ways of doing this, I came up with the idea of roads and factories. - This seemed to clearly explain my subject, so the project was assembled accordingly. Square Root Function Computer KENNETH YEAGER lI0l Jaclrsonville High School Jacksonville Sponsor: Richard N. Ommen .gg 1135 .. fs 1 : SQUARE RUUT FUNCTIDN COMPUTER Ll l.l The purpose of this project was to design and construct digital circuitry to extract square roots from numbers. The binary number system was chosen because of its efficiency in digital computers. Further experiments with binary re- sulted in a method similar to the mechanical square root function. This method was the basis of the circuit design. Like the mechanical function, the computer operates in cycles. The number whose square root is desired is divided into pairs on each side of the decimal point. On the first cycle, the first pair is placed in a memory register. The computer then substracts 1 from this and puts a 1 in the first place of the quotient. On each successive cycle, the next pair is put in the register with the first and a number is determined by multiplying the quotient by 4 and adding 1 . If this number is smaller than the number in the regis- ter, it is subtracted from the register and a 1 is placed in the next place of the quotient. If it is larger, it is dropped and a zero is placed in the quotient. In this manner the quotient is determined place by place. Greater accuracy can be at- tained by adding more circuits. The computer was built with electromagnetic and mag- netic reed relays to demonstrate its operation. Although the actual circuits were designed for these components, the logical design could be easily adapted for use of transistors. Flip-Flop Computer DOROTHY YETTER KATHY 'FUCHS The Immaculate High School Chicago Sponsor: Sister Mary lnezetta, BVM 9 Our project was primarily aimed at the mathematics directly connected with computers. The binary number sys- tem was first to be studied. This system operates on the same basis as our own system, base ten. The computations, addition, substraction, multiplication, and division, are dem- onstrated on the small model of a binary digital computer that we built. We adapted a basic circuit used in all digital computers called the flip-flop. The components of our own flip-flop consisted of resistors, diodes, and capacitors which aided the transistors in acting as electronic switches. Since we used only six of these, we were only able to reach the number sixty-three. In computer language, the binary number system is broken up used for its simplicity. This way every program is into yes-no questions. But to accomplish these programs successfully in insertion and processing, another form of mathematics is involved, Boolean Algebra, or the logic of computers. In this logic, function, or combinations of com- binations, of binary variables are used. Computers in general involve four main processes: input, processing, memory, and output. A demonstration of these is shown on a small supplement to our computer, a double card reader. This apparatus can not only read a card, but also can correct multiple choice tests. Computers are becoming the heart of man's life. But computers can not run by themselves and thus man has to supply the brains. By our project we have acquired a begin- ning into the dynamic life being built before us. What are Conic Sections? TOM WOLFF Northwood Junior High School Besides being of scientific importance, conics are seen every day. The object of my science project was to learn in detail the scientific, mathematical and practical charac- teristics of the basic for conics: the circle, the ellipse, the byperbola, and the parabola.

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