Right. I was hoping that was the case, or my understanding of transcendental (heck, irrational) numbers was way off.
On the other hand, you can demonstrate pi, just not draw a line of length pi, with a compass (i.e., point to the circumference of a circle). My mind is trying to create some infinite-regress of seashell spirals to demonstrate e similarly...
You *can* draw many irrational numbers, just not transcendental numbers. You can, for example, construct the square root of two (the diagonal of a square).
Algebraic numbers are the numbers that are roots of some polynomial equation (with integer coefficients not all equal to zero). Transcendental numbers are the ones that aren't algebraic.
I don't really have a good enough intuitive understanding of e to have an idea how to demonstrate it geometrically.
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On the other hand, you can demonstrate pi, just not draw a line of length pi, with a compass (i.e., point to the circumference of a circle). My mind is trying to create some infinite-regress of seashell spirals to demonstrate e similarly...
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Algebraic numbers are the numbers that are roots of some polynomial equation (with integer coefficients not all equal to zero). Transcendental numbers are the ones that aren't algebraic.
I don't really have a good enough intuitive understanding of e to have an idea how to demonstrate it geometrically.
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