Ask Can a practical geometry be constructed from A circle. Let us begin by making a circle w/ the forefinger or index finger and the thumb. This circle can be gradually contracted to approach a geometrical point. It can be imagined that the circle ever approaches a point-having motion-but never attains the point. continue, We can, also, begin w/ the circle made by our forefinger and thumb and expand it. If it expands along a straight line of course it becomes a plane. The circle can, also, generate in three dimensions. continue, Let us make a globe or sphere w/ two poles or holes. We generate the globe by moving the circle along and at right angles to a prearranged or given circle. The circle then expands and then contracts to form a globe with two poles or holes. It is possible that this can be defined as an electric sphere. continue, We can, also, make or construct a magnetic sphere. The method is similar. We move the circle from the origin to the left and describe a cylinder. We then turn the circle in an arc again and reverse the direction moving twice as far to the right. Turning the circle in an arc again we make it smaller and move to the left and return to the origin. On a flat surface this looks like two rubber bands laid parallel to each other. Thus we have described a magnetic sphere or globe. continue, Ask Is there a gravitational sphere like the above spheres? Well, my intuition, my imagination, my invention tell me that such a sphere is closed for a gravitational body at rest. It is possible that everything is in motion, however, and that the gravitational body has poles or holes. But poles suggest a straight line between them. I think this system leads to a theory of motion using/employing the poles for straight line motion. continue, Ask If it may be valid or sound that a body in motion has gravitational poles, and a body generating gravitational poles is in motion. Ask If electrical and magnetic spheres having poles may, also, possess a form of motion or of direction. continue Ask If equation E.M.G. like 2.4.8. is valid? E.M. = M.E. appears to represent oscillating motion, that is, wave motion. Ask Can you verify? Copyright 1990 Lynn H Fisher, earlier work Copyright 1976 Lynn H Fisher. Addenda Copyright 2002 LHF. continue, Page Two, By intuition, imagination, and invention I can conceive that an electron which is negative outside may be positive inside. I get the idea from magnetism which is divided into North and South poles. But the magnet is both separate, and together. This is called a paradox. It appears then that in an electron there may be a paradoxical middle separating, and connecting a supposed positive inside with a negative outside. If this sytem integrates well, and suggests simplicity it should be accepted. It is also possible that at the core or center of an electron there is antigravitation. The question can be asked: Why doesn't gravitation collapse if it is only a force directed inside? The antigravitation may act for a very short distance. There may also be a paradoxical middle separating, and connecting gravitation with antigravitation. Paradox is complex of course because there are two parts. I expect you can imagine marriage. Well, a paradox is a married mind like a magnet. It is a middle. From the middle you move in course outside or inside. continue, I, also, ask another question which experiment may answer. I ask: Does a particle moving at or near the velocity of light have an inclination to separate into two new particles-one fore, and one aft. My intuition, my imagination, my invention suggest that such a particle would begin in the guise of a circle. Moving at near light velocity it becomes perhaps like a circle separating from a circle. Imagine then two circles intersecting in a middle. (This thought is original or independent creation with myself.) This may be like Einstein's concept of a flattened mass at near light velocity. The two new circles then have centers that may be like poles of focuses like a magnet. continue, I ask: As the circles separate: Do two new particles form? What is the nature of these particles? This is a geometrical model which I was inspired to invent about or before 1965. continue, Page Three, Attraction and Repulsion in Circular Geometry, The mathematical professional already knows what a normal to a curve is. So I will explain for the layman. A normal line be it known is at right angles or perpendicular to a tangent to a curve. Normals in this system are employed to explain direction of motion or inclination toward motion. continue, As a figure to represent repulsion I have taken for use the hypocycloid. (illustration on original work) It appears that where the normals congregate or concentrate is the inclination toward motion. It appears then that if the curves face outward, the normals to the curve focus in general in the direction of the curve. I give as an illustration the headlamp of a car. This is a parabola. But this isn't an exact illustration because light rays move from the focus of the parabola here and are reflected forward from the parabola. Instead in this system the normals to the curve-such as a parabola-congregate and perhaps intersect within the space surrounded by the curve. continue, Thus in this system a circle or ellipse represents gravitation. As is easily perceived the normals to the curve-the many radius or radii-meet at the center of the circle. This appears to be the inclination or direction of motion. If there be such a thing as antigravitation, perhaps, at the center of an electron, you can imagine, perhaps, it resembles a hypocycloid in three dimensions. And repels falling gravitation for a short distance. continue, It is possible by intuition and imagination to invent the idea or concept of repulsion for two electrons. Imagine two parabolas facing in opposite directions or away from each other. This appears as the direction of motion with the congregates of normals facing away from each other. (illustration in original work) This is an example of repulsion. continue, Page Four, Thus a circle or an ellipse whether of gravitational, electrical, or magnetic bodies appears to represent attraction or attractive forces. A hypocycloid in the instance of magnetism or gravitation appears to represent repulsive forces. It is possible that two parabolas both facing away represent repulsion for two electrons. I have also made the effort to consider for this system twin hyperbolas to represent magnetism. This idea appears to include paradox or both attraction and repulsion and appears new at this time. Perhaps, this idea can be worked out with benefit. continue, Thus repulsion is attraction toward outside. Attraction is an inclination or direction toward the inside. This appears very clear and with simplicity and elegance. continue, (Following is my work on Like Charges or Poles Repel and Unlike Charges or Poles Attract) Something I came upon or invented and discovered like the birth of a baby about or before September 1965 should I believe be included here. I sat down at the dining room table of my home in Pierce County, Wisconsin near Ellsworth again in September 1965. I took accounting of ideas and concepts I had invented and discovered prior to that time and placed them on paper. I recall thinking then of the following which I thought very simple: It is a geometrical explanation of Like Charges or Poles Repel, and Unlike Charges or Poles Attract. If the product (+) represents repulsion, then the equation (-)x(-)=(+) represents Like Charges or Poles Repel. The similar reasoning holds true for (+)x(+)=(+). This appears to mean "inside" times "inside" equals "outside." (On the other hand) If the product (-) represents attraction and inside, then (+)x(-)=(-) represents Unlike Charges or Poles Attract and male and female attract-while men repel or disagree. continue, This is my work Copyright 1990 from Circular Geometry. My previous work on this subject is Introduction to Circular or Fisherian Geometry 1976. The name Lynniann Geometry sounds correct to me.

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