Most religions have in common, a chief prophet; a priesthood, a means or object of sacrifice, and a goal that reaches into the supernatural, and heretics. Judaism, for example, offers Moses, the Levitical Priesthood, Animal sacrifice, eternity, and heresies. Mathematics offers Euclid (Prophet), Mathematics Professors,(High Priests), Students being tested (Animal sacrifice), Infinity (Eternity), and heretics, (people who ask questions).

Let's examine some of the accepted "fundamentals" of this "religion," called "Mathematics." 1. The basis of all Mathematics is "FAITH." Axioms and Postulates are the "assumptions" upon which all Mathematics rests. "Assumptions" are the articles of Faith, upon which the religion of Mathematics builds its dogma. Postulate #2 is quoted in many textbooks, as an article of Faith. Yet when applied, it is denied vehemetly. The Postulate states: "A straight line may be drawn to any required length." I am given radius r, and line c whose "required length" is Pi times the diameter. "Can't be done..." negating Postulate #2.

2. The three "impossible" problems of geometry for example:

"Each construction must remain in the Euclidean plane," and, "What was demanded was in each case an exact construction by straight-edge and compass used in the manner prescribed by Euclid..."

Excuse me.....Hippocrates of Chios offered two of the three "impossible" problems approximately 440 B.C., Hippias offered the third, Trisection of the angle, approximately 420 B.C., Euclid (the prophet of Mathematics) WASN'T BORN YET. How does this man rate such influence, that he can set standards for Mathemeticians before he was even born? I can understand how his discoveries would affect the efforts made after his time..... but BEFORE his time??? I don't think so.

This reminds me of those who attempt to hold Lot accountable to the standards of the Law of Moses, or Christ, and say that Lot was a terrible man because he offered his daughters to the lusting crowd, at Sodom. But Lot was not under the law of Moses, nor was he a Christian. Those standards did not come into existence for centuries, and Lot was not held to such standards. Paul tells us in Romans 5:13 that sin was not imputed where there is no law. Lot may have "done the deed," but there was no law, thus no sin imputed to him. And Peter called him a "righteous man." (2Pet 2:7-8)

3. The value of Pi can be calculated to infinity, and cannot be constructed using straight-edge and compass.

Prior to this time, the Hebrew influence may have been significant, in the understanding of the value of Pi. The Hebrew books of I and II Chronicles, and I and II and Kings, written approximately 600 to about 550 B.C., in which Pi was figured to an approximate value of three. I may have an explanation of the understanding of "Pi and infinity," which would account for this.

It is possible that the "compass" of I Chronicles, relates to a thickness of a wall, which interially, will have one measurement, exterially will have another, but may be a ratio of three "average," measurement. This would be one way to account for the value of Pi being understood as "three." A second possibility is that they had no concept of Pi, but only of a relationship between a circle and its diameter.

A third possibility: I believe there is a side of "infinity" which implies being "bound." I call it "bound infinity." It deals with infinity which functions within, or between, parameters. "Understanding Infinity" and More About Infinity explain an understanding of "Pi and Infinity," which could have been known anywhere in the world Hebrew scholars were present. (I Kings 7:23, and II Chronicles 4:2); And beyond this I cannot assert anything. I am dealing only with Possibilities. But this "possibility" has more in touch with reality than ascribing "Euclidean" values to the problems.

Pi; An Article of Faith?

4. A Point has no dimension, a Line has no "width," or "thickness."

If points have no dimension, how can they generate a line? When a line is said to be drawn from "Point" A to "Point" B, is there an understanding as to whether the line meets at the "inside," "middle," or "outside" of the point? This becomes significant when drawing to a "press-fit."

And then, there are the of Heretics; those students who, upon rare occasion, dare to question the high priests of modern Mathematics. And there is plenty of reason to question. Remember the "empty set" of "set theory?" It was supposed to CONTAIN all sets which contained nothing? If it contains anything, how can it be empty? Remember "infinity?" That term is used to cover everything that requires a home, but has no parameters with which to build it one. Most often it should more correctly be labeled, "unlimited," or possibly "uncounted as yet." Take for example, the method usually offered to find the circumference of a circle, concerns itself with using straight-lined figures, expanding ever closer to the outer perimeter, to infinity, as "unresolvable." What they fail to understand is, the circumference IS THE LOCATION OF WHERE the "Infinity" lies with respect to that particular figure. The failure is in the use of "straight-line" construction to attain curved-line goals.

To stipulate that the value of Pi is "infinite," makes an equal claim that we know its limitation, i.e., "infinity." "Infinity" CANNOT be used as a limitation, but the high priests of Mathematics will have us heretics bound and sacrificed before admitting that such is the case.

1. DOUBLE THE VOLUME OF THE CUBE:
   • First step of construction.
   • Then construction completed.
   • Perspective drawing of cubes.
   • Perspective in color.
2. SQUARE THE CIRCLE:
   • Schematic For A Square Root
   • First Step to Square a Circle.
   • Second Step to square a Circle.
   • Third Step to Square a Circle.
   • Fourth Step to Square a Circle.
   • Squared Circle
3. TRISECT THE ANGLE:
   • Basic Layout for Trisection.
   • collapsed Altitude shows next step.
   • Trisected Base Angle shows Trisection.
   • Trisected Apex Angle shows Complete Trisection.

None of the problems constructed above are limited by a "Euclidean Plane," none adhere to some "out-there" philosophy of "infinity," and all depend upon "seeing" the thickness, or "width" of the line. Keep the Faith.

© 1997 Theophilus Book

E-mail Address:the_book_crypt@bigfoot.com