Stream

Join this community to post or comment

Paddy McCarthy

Videos/Pictures  - 
1
1
Add a comment...

ART KOSEKOMA

Videos/Pictures  - 
 
 
Розгортка чотирисхилого куполу (J4)
Развертка четырёхскатного купола (J4)
The Net of Square Cupola (J4)
#nets
#развертки
#polyhedra
#многогранники
#MATHARTWORK
#KOSEKOMA
 ·  Translate
2
Add a comment...

Zach Cox

Videos/Pictures  - 
 
When I was a child I used to read Science Fiction and fell in love with that and with science in general.

I can only imagine what impact the playlist below would have had on my mind as a high school student.

This series of videos should be shown to all high school students when they first encounter complex numbers and again to college students in any math class that first introduces complex numbers.

https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF
10
1
Brian Sherson's profile photoSteven Siew's profile photo
2 comments
 
Imaginary numbers are real because they are used to represent real physical phenomena. An imaginary (electrical) current will fry you to death if it's value is high enough. This is because the complex number representing the electric current is representing both magnitude and phase of the current. A purely imaginary electric current is just an electric current with a magnitude and its phase is 90degrees off the reference phrase.
Add a comment...

Paddy McCarthy

Videos/Pictures  - 
 
 
Intuition sucks!
Add this one to the Monty Hall problem as cases where the mathematically correct answer is at odds with most intuitive answers.
All dies are fair and six-sided but with differing numbers on each face. One die is said to be stronger, > than another if that ...
7
Paddy McCarthy's profile photoDouglas Kalles's profile photo
3 comments
 
+Paddy McCarthy aims? I am just asking a slightly different question. This "paradox" only shows you the results of several scenarios in which only 2 dice are compared at a time. I would wonder what would happen if all 4 dice were thrown together. What would the spread of that look like?
Add a comment...

Zach Cox

Videos/Pictures  - 
 
If that Taxi driver were an underemployed math major they would know all this beforehand and would have LEFT MORE ROOM TO STOP.

I am always leaving extra room in front of me, much to the exasperation of drivers behind me, sometimes even going as far as folks passing and 'tucking-in-front-of-me' at which point I have to slow down to reestablish the correct distance.

When this occurs I always make it a point to "Roll-My-Eyes" at the driver.
4
Add a comment...

Math

Videos/Pictures  - 
12
3
fizixx's profile photoSteven Siew's profile photo
2 comments
 
You spelled "spill my seed" incorrectly
Add a comment...

Isaac Calder

Videos/Pictures  - 
 
for those of you that have seen the 2 polyhedra constructed from 15 & 65 soccerballs, here is the next one in an infinite series of those polyhedra, this one with 175 soccerballs; the format of the 'animals' is like a rhombic dodecahedron (in the figure, each rhombus has 16 soccerballs; formula for the number of soccerballs N is (x being the order): N=x^3+24.x^2-29.x+19, the genus being g=x^3+72.x^2-121.x+66.
please be happy, everybody!...
8
Add a comment...

Isaac Calder

Videos/Pictures  - 
 
yesterday afternoon, while playing a bit with the famous fullerene C60 or soccerball, I obtained 2 curious nontrivial polyhedra by gluing 15 (respectively 65) C60 only through 6-gon faces, of which I post the 2 animations herewith.
15-C60= [V=708, F=416, E=1158; genus: g=18] &
65-C60= [V=2,796; F=1,712; E=4,746; genus: g=120]
symmetry in both cases is Th (tetrahedral complete w. horiz. reflect.)
please be well, everybody!..
13
1
Add a comment...

philippe roux

Videos/Pictures  - 
 
 
Last week the French mathematician Jean-christophe Yoccoz sadly died, he was a specialist of dynamical systems and was awarded by the Fields Medal in 1994 for his work. The billiards are good examples of the complexity of even simples dynamical systems, for example the Sinaï billiard modelizes the interaction of an atom (the broken line below) in a homogeneous gas (the red obstacle) . The behavior of the particle is so complex that only a probabilistic study of the evolution can be done , this is the basis of statistical physics.
#mathematics
15
1
Add a comment...

Isaac Calder

Videos/Pictures  - 
 
repost from Mar 31, 2015
yesterday I found this nice solid, a hecatondecahedron, whose faces are 80 congruent equilateral triangles & 30 congruent squares [V= 72, F= 110, E= 180]; all edges are of the same length, but its vertices are of 3 types: 24 of valence 4 (curvature= 60 deg), 24 of valence 5 (curv= 60 deg) & 24 of valence 6 (curv= - 90 deg); total curvature= 48*60+24*(-90)= 720 deg, as it should be... symmetry: Oh (octahedral complete w. horiz. reflection), the same of the cube & octahedron
please be well, you all!..
17
2
Add a comment...

Isaac Calder

Videos/Pictures  - 
 
and this is a nice polyhedron with a complicated name, namely expanded-joined-hexpropello-dodecahedron, every prefix being full of geometric information; by the way, it was not easy to construct...
please be happy, you all!..
face vector: [V=840, F=842, E=1,680] symmetry is T (tetrahedral chiral!) faces (in decreasing area):
60 (6-gons), all congruent; 12 (5-gons), all congruent; 630 (4-gons) of no less than 14 different kinds: 60+60+60+30+60+60+60+12+60+60+48+12+36+12; 140 (3-gons) of 3 kinds: 20+60+60
23
5
Isaac Calder's profile photoRefurio Anachro's profile photo
5 comments
 
Oooh. That's... Cool! Thanks for ridding me of yet another misconception! Now I need to figure out how that can happen. There's a beautiful example spinning right in front of my nose...

Heh, did you just amend your post? That should make it even easier, thank you!

There are so many kinds of faces! 
Add a comment...

Isaac Calder

Videos/Pictures  - 
 
4th (& this will be the last) solid of the infinite family which begins with 15, 65, 175 & now 369 soccerballs). In a previous post I had conjectured the formula N= x^3 + a.x^2 + b.x + c and I had found a, b & c. Unfortunately the said polynomial is not the most general 3rd degree one, which is N= a.x^3 + b.x^2 + c*x + d , whose coefficients can all be found only when one has considered the 1st 4 cases.
the final corrected formulae are:
N= 4.x^3 + 6.x^2 + 4.x + 1= (2.x+1)(2.x^2 + 2.x +1) & the genus:
g= 12. x^3 + 6.x^2 = 6.x^2(2.x+1)
voila! I thank you all for reading this and
please be happy you all! new subject in next post...
21
1
Sean Walker's profile photoP Grimm's profile photo
2 comments
P Grimm
 
Amazing
Add a comment...

Kevin Clift

Videos/Pictures  - 
 
 
Imaginary Numbers The Movie

Machine Learning Research Engineer Stephen Welch has recently finished his 13 part video series on Imaginary Numbers.

It took over a year, but the Imaginary Numbers Series is finally complete. By far the most labor intensive parts were part 1 and part 13. When I began the series I had no idea where it would end up. I originally planned on 6 parts, but the deeper I got into imaginary numbers, the cooler things got - and I just couldn't deal with telling an incomplete story.

I couldn't be happier with where the series ended up - I'm so happy I was able to talk about Riemann Surfaces. I'm sure a mathematician or two will take issue with my presentation (there's a reason Riemann Surface are a graduate level mathematics topic!), but I hope I was able to give a broad audience a taste for these beautiful mathematical structures without oversimplifying the meaning out of things.

More here (blog): https://goo.gl/sz49tI


Part 1: Introduction: https://goo.gl/Gn3mvI

Part 2: A Little History: https://goo.gl/Pf7H9Q

Part 3: Cardan's Problem: https://goo.gl/xHf1Su

Part 4: Bombelli's Solution: https://goo.gl/V1m0Nj

Part 5: Numbers are Two Dimensional: https://goo.gl/131CSk

Part 6: The Complex Plane: https://goo.gl/0cF6Xi

Part 7: Complex Multiplication: https://goo.gl/XRQFZR

Part 8: Math Wizardry: https://goo.gl/KoSwlf

Part 9: Closure: https://goo.gl/HS0bDN

Part 10: Complex Functions: https://goo.gl/miDdMm

Part 11: Wandering in Four Dimensions: https://goo.gl/q77KBJ

Part 12: Riemann's Solution: https://goo.gl/RG3eJ0

Part 13: Riemann Surfaces: https://goo.gl/xoDvXX

Playlist: https://goo.gl/ZBuEyC

Buy the Workbook: https://goo.gl/8a9hLi


Related post: https://goo.gl/jT1zlk

Image: Svjo https://goo.gl/mZi3L2
23
2
Christer Nyqvist's profile photoCliff Haman's profile photo
4 comments
 
This series is superb. The explanations are excellent and the narrative style is highly entertaining. The concepts are covered sensibly and logically with accompanying visuals that make the material highly understandable.

Add a comment...

Vineet George

Videos/Pictures  - 
10
3
Gianni Rossi's profile photo
 
Fool proof? Why are fools testing for primes in the first place?
Add a comment...

Isaac Calder

Videos/Pictures  - 
 
this is only a gif animation of the 175-augmented-C60 solid, which was spoken of here yesterday evening (175 soccerballs so nicely arranged (!) that they look like a ultra rhombic dodecahedron deserved of course better than a dry picture...)
please be well you all!..
17
3
P Grimm's profile photo
2 comments
P Grimm
+
1
2
1
 
Nice, that is taking some compute power
Add a comment...

Zach Cox

Videos/Pictures  - 
 
Excellent! (as always)
25
4
Gunjan Dixit's profile photo
 
Wow, thats great
Add a comment...

ART KOSEKOMA

Videos/Pictures  - 
6
Add a comment...

Math

Videos/Pictures  - 
 
“Shadows of Higher Dimensions”

• The 0-dimensional point is a shadow of a line…

• The 1-dimensional line is a shadow of a square…

• The 2-dimensional square is a shadow of a cube…

• The 3-dimensional sides of a cube are the shadow of an (unfolded) hypercube.
37
8
Tero Pulkkinen's profile photo
 
There was some nice math I found recently related to this picture. (f(x,y) == true) => (exists y.f(x,y)==true). This basically binds one of the variables.
Add a comment...

Zach Cox

Videos/Pictures  - 
 
The only paper I've ever given was not refereed but I can certainly imagine that this is probably pretty close.

https://mathwithbaddrawings.com/2016/09/14/if-nfl-referees-behaved-like-academic-referees/
Maybe “referee” isn’t the most fitting word after all.
3
Add a comment...

Math

Videos/Pictures  - 
16
2
Bruce Mincks's profile photo
 
The Platonic solids are "regular" in the sense that they derive a whole number of polygons as the faces of a solid inscribed in a sphere

https://plus.google.com/108657187448883149300/posts/W8gXvSUTfED

There are only five such solids, and given such a sphere, the iscosahedron and dodecahedron "resonate" among the same points. If you construct all five, you find that for starters, the tetrahedron's dimensions exclude any central point in that sphere by implying equal distances in four directions; eight actually, as you consider the perpendiculars to the center of all four faces.

https://docs.google.com/document/d/1TUcsW-f4WBPxkxzqPoA3EWa8GufJbG5Uey_wjwtdfFM/edit?usp=sharing
Add a comment...