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AdmaXAdMin
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Age : 46 
Mathematicks
Thu Jan 07, 2016 6:01 pm
ΓΕΝΙΚΟ,
ΘΕΜΑ - AdmaXAdMin
- Posts : 550
Join date : 2016-01-05
Age : 46
http://mathworld.wolfram.com/
Sun May 15, 2016 10:31 pm
http://mathworld.wolfram.com
-
http://www.wolframalpha.com
-------------------------------------------
https://www.encyclopediaofmath.org
----------------------------------------------
Manhattan GandhiLeveL V
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Join date : 2016-01-09
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Location : R'Lyeh
Regular Polytopes in All Dimensions
Thu Jun 16, 2016 9:19 pm
What's the pattern in this sequence?
, 5 , 6 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , ...
John Baez's Stuff
Geometry
φ Ron Knott
Regular Polyhedra from the Web.
----------------------------------------------------------------------------
the tetrahedron | the cube | the octahedron | the dodecahedron | the icosahedron |
Higher-Dimensional Polytopes:
The 'hypertetrahedron' '4-simplex' | The 'hypercube ('tesseract') |
The edges are bulging out on because they're drawn in a 3-sphere!
You can also draw the pictures in the more familiar 'flat' style
:
--------------------------------------------------------------------
The 'hyperoctahedron'/'16-cell' | The 'hyperdodecahedron' |
The 'hypericosahedron' | 600 cell Cell-first projection of the 600-cell into 3D |
3D projection of a 600-cell. | the 24-cell/24 octahedral faces |
This is a denizen of the 4th dimension with no analog in lower dimensions:
--------------------------------------------------------------------------------------------
4-dimensional space is the peak of complexity as far as regular polytopes go.
In 5 or more dimensions, there are only three regular polytopes:
In 5 or more dimensions, there are only three regular polytopes:
# There is a kind of hypertetrahedron, called the 'n-simplex', having (n+1) faces, all of which are (n-1)-simplices.
# There is a kind of hypercube, called the 'n-cube', having 2n faces, all of which are (n-1)-cubes.
# And there is a kind of hyperoctahedron, called the 'n-dimensional cross-polytope', having 2n faces, all of which
For Further Study : Eric Weisstein's Mathworld website. :: Platonic solids and 4d geometry.
/ George Hart's Encyclopedia of Polyhedra, H. S. M. Coxeter, Regular Polytopes, 3rd edition, New York, 1973.
- Manhattan GandhiLeveL V
- Posts : 565
Join date : 2016-01-09
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Re: Mathematicks
Thu Jun 16, 2016 9:45 pm
This Week's Finds / Azimuth
This Week's Finds in Mathematical Physics
-----------------------------------------------
the butterfly, the gyroid & the neutrino:
-----------------------------------------
Part 2 | Part 3 | Part 4 | Part 5 |
Part 6 Part 7 | Part 8 | Part 9 |
Part 10
Rolling Circles 3
Holodeck Games and CCCs
This Week's Finds in Mathematical Physics
-----------------------------------------------
the butterfly, the gyroid & the neutrino:
-----------------------------------------
_tiling.png) |  |
Part 6 Part 7 | Part 8 | Part 9 |
Part 10
Rolling Circles 3
Holodeck Games and CCCs
- Manhattan GandhiLeveL V
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Join date : 2016-01-09
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Poincare Hyperbolic Disk
Sun Jun 26, 2016 5:47 am
- Manhattan GandhiLeveL V
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hypercubes
Sun Jun 26, 2016 9:34 pm
hypercubes
hypercube 1
Hypercube /mathemamovies
Unwrapping a tesseract
--------------------------------
Corpus Hypercubus
--------------------------------
--------------------------------
hypercube 1
Hypercube /mathemamovies
Unwrapping a tesseract
--------------------------------
Corpus Hypercubus
--------------------------------
 | A net of a tesseract |
- Manhattan GandhiLeveL V
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Da Vinci Kepler polyhedra
Sun Jun 26, 2016 9:35 pm
A skeletal polyhedron (specifically, a rhombicuboctahedron)
drawn by Leonardo da Vinci to illustrate a book by Luca Pacioli
Johannes Kepler's Polyhedra
- Manhattan GandhiLeveL V
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Klein , Felix (1849-1925) & The man with 1,000 Klein Bottles UNDER his house
Sun Jun 26, 2016 9:35 pm
http://torus.math.uiuc.edu/jms/Images/klein.html
Leo Moser wrote:A mathematician named Klein
Thought the Möbius Loop was divine
Said he, "If you glue
The edges of two
You get a weird bottle like mine.
The man with 1,000 Klein Bottles UNDER his house
Klein Bottles - Numberphile
Acme Klein Bottle !
Hunt for the Elusive 4th Klein Bottle
There once was a bottle called Klein
That had such a clever design
It would turn inside out,
Which created some doubt
When it came to decanting the wine.
- Manhattan GandhiLeveL V
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Benoît Mandelbrot fractals and Roughness
Mon Jun 27, 2016 5:31 am
Benoît Mandelbrot IBM Short
The Nature of Roughness in Mathematics, Science and Art
Mandelbrot Zoom 10^227 [1080x1920]
https://www.youtube.com/watch?v=PD2XgQOyCCk
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John H. Conway , Life, Death and the Monster
The Nature of Roughness in Mathematics, Science and Art
Mandelbrot Zoom 10^227 [1080x1920]
https://www.youtube.com/watch?v=PD2XgQOyCCk
-----------------------------------------------------------------------
John H. Conway , Life, Death and the Monster
- Manhattan GandhiLeveL V
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Re: Mathematicks
Wed Jun 29, 2016 10:07 pm
https://www.youtube.com/watch?v=WabHm1QWVCA
https://www.youtube.com/watch?v=REeaT2mWj6Y
Inconvenient truths about sqrt(2)
https://www.youtube.com/watch?v=REeaT2mWj6Y
Inconvenient truths about sqrt(2)
- Manhattan GandhiLeveL V
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The Riemann Hypothesis
Sat Jul 16, 2016 2:14 am
http://www.aimath.org/WWN/rh/
The Riemann Hypothesis
The Key to the Riemann Hypothesis - Numberphile
------------------------------------
zeta function
Plot of the Riemann zeta function
along the critical line
for real values of t running from 0 to 34.
---------------------------------------------
Riemann zeta function showing the pole z=0
& 2 zeros on the critical line.
The Riemann Hypothesis
The Key to the Riemann Hypothesis - Numberphile
------------------------------------
zeta function
Plot of the Riemann zeta function
along the critical line
for real values of t running from 0 to 34.
---------------------------------------------
Riemann zeta function showing the pole z=0
& 2 zeros on the critical line.
- Manhattan GandhiLeveL V
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Monstrous Moonshine John H. Conway
Sat Jul 16, 2016 3:00 am
j-Function
------------------------------------------------
: WHAT IS...The Monster?
Monstrous Moonshine
Life, Death and the Monster - Numberphile
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: WHAT IS...The Monster?Monstrous Moonshine
Life, Death and the Monster - Numberphile
A mathematician is a device who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.
Mathematics is the most beautiful and most powerful creation of the human spirit. Mathematics is as old as Man.
- Manhattan GandhiLeveL V
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H. S. M. Coxeter , Escher , Circle Limit III
Wed Dec 14, 2016 10:30 pm
- Manhattan GandhiLeveL V
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Hyperbolic Cube
Wed Dec 14, 2016 11:13 pm
A hyperbolic version of the Euclidean cube.
- Code:
When you play, you don't ask "why" you are playing – you just play.
Play serves no moral code except that strange code which, for some reason, imposes itself on the play....
You will search in vain - through scientifick literature for hints of motivation.
And as for the strange "code" observed by scientists, what could be stranger than an abstract regard for truth in a world
which is full of concealment, deception, and taboos? … In submitting to your consideration the idea that the mind is at its
best when playing, I am myself playing, and that makes me feel that what I am saying may have an element of truth..
DelearthLeveL V- Posts : 541
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Magic Squares Melancholia I , Frenicle's 880 John Conway Albrecht Dürer
Sun Mar 11, 2018 7:00 pm
- DelearthLeveL V
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z->z^2+c
Mon Jun 18, 2018 9:00 pm
The first published picture of the Mandelbrot set, by
Robert W. Brooks and Peter Matelski in 1978
> Mandelbrot set on the IBM 1401 computer
- DelearthLeveL V
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Aaron Sloman
Thu Mar 21, 2019 9:30 pm
- AdmaXAdMin
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Re: Mathematicks
Sun Oct 13, 2019 6:31 pm
In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful
that the truth of a theorem is almost seen at a glance - [ from Martin Gardner "Mathematical Games ", in
Scientific American October 1973; also quoted in Roger B. Nelson, Proofs Without Words: Exercises in Visual
Thinking (1993), "Introduction", p. v ]
- DelearthLeveL V
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Τετραγωνισμὸς παραβολῆς ~ Archimedes' squaring of a parabola
Thu Dec 12, 2019 7:00 am
- DelearthLeveL V
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On the Number of Primes Less Than a Given Magnitude Bernhard Riemann
Tue Nov 10, 2020 8:00 am
Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse
by Bernhard Riemann
Riemann's manuscript
Transcription
English translation
November 1859
by Bernhard Riemann
Riemann's manuscript Transcription English translation November 1859
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