(no subject)

[learnedax]

New York plans to construct a tower 1776' high for technically symbolic reasons. Too bad they're not comemorating the Whiskey rebellion, or we could get a tower of e furlongs. Wouldn't that be much nicer?

Comments

[katkt.livejournal.com]

Or, well, slightly less than e furlongs. Almost .7921 inches less. You've got to be careful with those transcendental numbers...

[metahacker.livejournal.com]

I want to see the guy whose ruler has e marked on it accurately...

(Hmm, good question, is there a geometric way to derive e precisely?)

[katkt.livejournal.com]

(No. At least, if you take "geometric way" to mean "means to construct using a compass and straight-edge", then no. Transcendental numbers can't be constructed with a ruler and compass. I imagine that you could construct a tool to let you do this, in much the same way that you can construct a tool that lets you square a circle...)

[metahacker.livejournal.com]

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...

[katkt.livejournal.com]

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.

[siderea]

You know, it's pretty much impossible to google on "e". Hrmmmm.

[katkt.livejournal.com]

But you can find it if you look in the right places.

[learnedax.livejournal.com]

Yes, or you could just for "number e" and turn up all sorts of interesting stuff.

[learnedax.livejournal.com]

Sure, you just need a hyperbolic compass...

You could rig up springs with the right coefficients, but that's cheating. You could demonstrate Pi and then derive e from it, but that's unsatisfying. You could could iterate triangles based on the ratio expansion, but that's an approximation.

Of course, in the end a geometric method can still only define it as precisely as the precision of the tools available, in our world.

[its-just-me.livejournal.com]

sigh.....