Draw a circle. O That’s good enough. Now, within the circle but close to its circumference, draw a polygon of any number of sides (say n sides). That’s good. Draw another polygon with n sides on the outside of the circle, but again close to the circumference of the circle. Great! Stay with me now. Check the perimeters of both polygons. Obviously, the perimeter of the one outside the circle will be greater than the circumference, whereas the perimeter of the polygon inside the circle will be less than the circumference. Somewhere between the two, the circumference has a value that neither polygon equals. However, it is possible to make the two polygons come close to the circumference. Just add sides (i.e., a larger n). From the outside, the polygon will shrink toward the circumference. From the inside the polygon will grow.
Of course, as polygons, neither the inside nor the outside figure will exactly match the circumference of the circle, but both will get infinitely close as you add sides. That was Archimedes’ thinking when he tried to pin down the value of π, an irrational number (a number that can’t be put in an exact fraction).
Much of what we do daily is, like pi, irrational. We would all have difficulty putting relationships in exact ratios. What do we say? “Well, he’s 3 to my 5.” “She’s definitely a 7 to my 11.” “Gosh, now that I think about it, I would say I am definitely 5/9 of our relationship.”
No, we can’t pin down relationships just as we can’t ultimately pin down pi. But we can use Archimedes’ method and reasoning to get close. Both polygons have to move toward each other, never quite meeting at the circumference of the intervening circle, but approaching a good approximation. That’s about all we can hope for in understanding human relationships, a good approximation arrived at after adding an indefinite number of sides.
Of course, as polygons, neither the inside nor the outside figure will exactly match the circumference of the circle, but both will get infinitely close as you add sides. That was Archimedes’ thinking when he tried to pin down the value of π, an irrational number (a number that can’t be put in an exact fraction).
Much of what we do daily is, like pi, irrational. We would all have difficulty putting relationships in exact ratios. What do we say? “Well, he’s 3 to my 5.” “She’s definitely a 7 to my 11.” “Gosh, now that I think about it, I would say I am definitely 5/9 of our relationship.”
No, we can’t pin down relationships just as we can’t ultimately pin down pi. But we can use Archimedes’ method and reasoning to get close. Both polygons have to move toward each other, never quite meeting at the circumference of the intervening circle, but approaching a good approximation. That’s about all we can hope for in understanding human relationships, a good approximation arrived at after adding an indefinite number of sides.
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