๐งต Untitled Thread
Anonymous at Mon, 18 Mar 2024 23:19:38 UTC No. 16085665
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?
Anonymous at Mon, 18 Mar 2024 23:22:36 UTC No. 16085670
>>16085665
How are you going to draw e^x using just geometric tools?
Anonymous at Mon, 18 Mar 2024 23:25:28 UTC No. 16085675
>>16085670
I'm sure Galileo or our newton had some kind of contraption that could do this
Anonymous at Mon, 18 Mar 2024 23:42:30 UTC 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?
Anonymous at Mon, 18 Mar 2024 23:54:12 UTC 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?
Anonymous at Tue, 19 Mar 2024 00:24:25 UTC No. 16085753
>>16085665
god I hate mathematics
Anonymous at Tue, 19 Mar 2024 01:01:04 UTC No. 16085794
>>16085665
"geometrically" is a metamathematical term and therefore it means nothing mathematically to say that e has no "geometrical" definition.
Anonymous at Tue, 19 Mar 2024 01:02:55 UTC No. 16085797
>>16085665
define e with pen and compass
i can do it but im not going to show you how
Anonymous at Tue, 19 Mar 2024 01:54:57 UTC No. 16085837
>>16085665
Neither e nor ฯ are "numbers", they are infinite series aka. algorithms.
https://njwildberger.com/
Anonymous at Tue, 19 Mar 2024 01:59:02 UTC No. 16085845
Anonymous at Tue, 19 Mar 2024 02:03:47 UTC No. 16085855
>>16085797
You need to do it in a finite amount of time, you dumbass.
Anonymous at Tue, 19 Mar 2024 05:33:08 UTC 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.
Anonymous at Tue, 19 Mar 2024 07:28:59 UTC No. 16086128
>>16086045
Not a parabola
https://en.m.wikipedia.org/wiki/Cat
Anonymous at Tue, 19 Mar 2024 08:15:58 UTC 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.
Anonymous at Tue, 19 Mar 2024 09:30:57 UTC No. 16086204
>>16085665
>but if e is the integral of the function e^x
this part literally makes no fucking sense.
Anonymous at Tue, 19 Mar 2024 15:58:54 UTC No. 16086652
Geometrical pi (in contradistinction with analytical pi) is not an unique real number unless you fix a metric and definition for "circunference".
Anonymous at Tue, 19 Mar 2024 20:41:40 UTC No. 16087004
>>16085696
>>16085712
I'm dying