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/sci/ - Science & Math

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16085665 No.16085665 [Reply] [Original]

I heard some mathematician say that e isn't geometrically defined unlike pi. but if e is the integral of the function e^x that's the same as saying it's the area of a shape two perpendicular sides and a curve of y=e^x between them. how is that not a geometric definition?

>> No.16085670

>>16085665
How are you going to draw e^x using just geometric tools?

>> No.16085675

>>16085670
I'm sure Galileo or our newton had some kind of contraption that could do this

>> No.16085696

>>16085665
>I heard some mathematician say that 7 isn't geometrically defined unlike pi. but if 7 is the integral of the function f(x)=7 from 0 to 1, that's the same as saying it's the area of a shape two perpendicular sides and a curve of y=7 between them. how is that not a geometric definition?

>> No.16085712

>>16085665
>I heard some mathematician say that e isn't geometrically defined unlike pi. but if sqrt(e) is the side length of a square with area e, that's the same as saying it's the area of a shape two perpendicular sides. how is that not a geometric definition?

>> No.16085753

>>16085665
god I hate mathematics

>> No.16085794

>>16085665
"geometrically" is a metamathematical term and therefore it means nothing mathematically to say that e has no "geometrical" definition.

>> No.16085797

>>16085665
define e with pen and compass

i can do it but im not going to show you how

>> No.16085837

>>16085665
Neither e nor π are "numbers", they are infinite series aka. algorithms.
https://njwildberger.com/

>> No.16085845
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16085845

>>16085837
>>16085753
>>16085794

>> No.16085855

>>16085797
You need to do it in a finite amount of time, you dumbass.

>> No.16086045

>>16085665
e has the geometric shape of half of a parabola

>>16085797
You need a pendulum, not a pen and compass, to draw a parabola or exponential.

>> No.16086128

>>16086045
Not a parabola
https://en.m.wikipedia.org/wiki/Catenary

>> No.16086149

>I heard some mathematician say that e isn't geometrically defined unlike pi.
they are brainlets. I guess they say it is analytically defined but analysis is just geometry (linear algebra too despite it is called algebra)
play around with this tool:
https://www.geogebra.org/m/unEFgDrf
e is defined as the only number a > 1 for which the area confined by the lines x=1, y=0, x=a and the curve y=1/x is equal to one.

>> No.16086204

>>16085665
>but if e is the integral of the function e^x
this part literally makes no fucking sense.

>> No.16086652

Geometrical pi (in contradistinction with analytical pi) is not an unique real number unless you fix a metric and definition for "circunference".

>> No.16087004
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16087004

>>16085696
>>16085712
I'm dying