pi

Pi is defined as the ratio of the circumference to diameter of a circle, which is always 3.141593..... It shows up in many formulas in science and engineering which are not obviously related to circles.

Brandon9000 wrote:

Pi is defined as the ratio of the circumference to diameter of a circle, which is always 3.141593..... It shows up in many formulas in science and engineering which are not obviously related to circles.

Is it 3.14.. because it is derived from a curve?

John Jones wrote:

Brandon9000 wrote:

Pi is defined as the ratio of the circumference to diameter of a circle, which is always 3.141593..... It shows up in many formulas in science and engineering which are not obviously related to circles.

Is it 3.14.. because it is derived from a curve?

No one who has ever lived has known why it has that value, it just does.

Pi always has to do with the relationship of a circle and its diameter. Circles and lines do not exist in the physical universe--they only exist in the minds of people. It is equally silly to contend that "no one knows" why the ratio is what it is. A geometer conceives of a circle, and then conceives of a diameter. The circle is an infinite number of points which occupy no space and describe a line all of the points of which are equidistant from a central point. Determining the ratio of the length of the line which forms the circle to the diameter (a line describing the distance between any two points of the circle which are exactly 180 degrees of arc apart) is simply a mathematical tool. Circles and lines are simply mental constructs which serve as tools in thought experiments. They are not real, they are only mental constructs.

Which mental constructs have now occupied more of my attention than they merit.

You are begging the question. You say curves and lines are constructs but do not say why it is possible to make pi from curves but not from straight lines? Please occupy your attention to this.

you can form a circle out of straight line segments and as the number of segments approaches infinity you will approach pi as the ratio. k?

stuh505 wrote:

you can form a circle out of straight line segments and as the number of segments approaches infinity you will approach pi as the ratio. k?

When i was bored in mathematics or science classes (which was usually the case), i would laboriously create "circles" through the use of straight line segments in my notebooks. None of the teachers ever got it--they were boring and even drawing a series of lines was more interesting than what they were foisting on me.

I sometimes regret that i did not apply myself more to math and science, but it probably would not have made a difference in my life. I always loved geometry, though, because i could draw it . . .