Everyone has patterns in their charts. They're called aspects, and they are noted by angles: 60°, for example, is a sextile. 180° is known as an opposition. A square, just as you learned in geometry, is 90°, and so on.
The astrological chart used to be developed in a square format, like the one shown on the following page:
http://www.archaicastrology.org/horary/
(I didn't take time to see the quality of the page since that wasn't the motive for my heading there. This was the best and most accurate example of old chart wheels as they used to be developed.)
As a result, the 1st, 4th, 7th, and 10th houses became known as the angles of the chart, also consistent with geometric thinking related to the chart itself. Today, the chart wheel for Western astrology is usually the 360° circle that is divided into 12 houses (these are the formulas to which I had referred; there are many depending on the house system). Hypothetically, each house has 30°; but the house sizes will vary in each chart depending on the house system used.
From the way you asked the question, it seems like you're trying to understand this based on graphic symbols of the aspects rather than understanding what an aspect is and the *guidelines* used for orbs based on those aspects. Some astrologers will be more rigid in sticking to a certain guideline for orbs. Others will be more flexible. I suppose you could say the choice of rigid or flexible orbs is based on the astrologer's experience.
The math beyond the geometric patterns used as one notes the angles between aspects in the chart wheel has to do with the formulas that are based on the house systems. Been There wrote earlier today about the hand calculations that she said are about 2 hours in calculation. I usually was able to create a chart by hand in 90 minutes, but I don't hand calculate anymore since I have a computerized program that can turn out a chart for me within 90 seconds at the most. If I am testing a computer program for accuracy, I will test it against my own hand calculations, however. But I have not delved into the trigonometry in hand calculation, preferring to use the tables to save myself the grief since I do tend to be more right-brained. I would rather ensure that the calculations I do are precise rather than making errors in calculation in areas like trig. I know my limits.
In re to physics, Rob Hand writes, "People who are familiar with mathematics or physics will recognize that what I am describing has some resemblance to a vector. A vector is a quantity that also has a direction... The planets act like vectors in that they set up stress patterns in the zodiac. And when the planets are in certain significant angles to each other (the aspects), which are derived by dividing the full 360° circle by small whole numbers, they set up vibrations or wave patterns in the zodiac... The planets, like vectors, have a quantitative stress, and more important, a qualitative stress, in a certain direction... We can consider all planets approximately equal quantitatively, except possibly the Sun and the Moon may be stronger. At any rate, we assign all the planets a value of one unit. Such vectors are called 'unit vectors.'"
I agree, btw, that one does not need psychic ability for astrology, but each astrologer is unique, just as many other professionals are in their own fields.