Start a hangout

All communitiesRecommended for you

## Stream

Join this community to post or comment

Join community

### ART KOSEKOMA

Videos/Pictures -Розгортка чотирисхилого куполу (J4)

Развертка четырёхскатного купола (J4)

The Net of Square Cupola (J4)

#nets

#развертки

#polyhedra

#многогранники

#MATHARTWORK

#KOSEKOMA

Развертка четырёхскатного купола (J4)

The Net of Square Cupola (J4)

#nets

#развертки

#polyhedra

#многогранники

#MATHARTWORK

#KOSEKOMA

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

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

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.

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

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.

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...

### Isaac Calder

Videos/Pictures -for those of you that have seen the 2 polyhedra constructed from

please be happy, everybody!...

**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

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

please be well, everybody!..

**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

#mathematics

**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

yesterday I found this nice solid, a

please be well, you all!..

**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 & octahedronplease be well, you all!..

17

2

Add a comment...

### Isaac Calder

Videos/Pictures -and this is a nice polyhedron with a complicated name, namely

please be happy, you all!..

face vector: [V=840, F=842, E=1,680] symmetry is T (

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

**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

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!

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...

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

2 comments

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

4 comments

Cliff Haman

+

1

2

1

2

1

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

+

5

6

5

6

5

Fool proof? Why are fools testing for primes in the first place?

Add a comment...

### Isaac Calder

Videos/Pictures -this is only a

please be well you all!..

**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

2 comments

P Grimm

+

1

2

1

2

1

Nice, that is taking some compute power

Add a comment...

### ART KOSEKOMA

Videos/Pictures -Трансформації куба

Трансформации куба

Transformations of Cube

#transformations

#трансформации

#polyhedra

#многогранники

#MATHARTWORK

#KOSEKOMA

Трансформации куба

Transformations of Cube

#transformations

#трансформации

#polyhedra

#многогранники

#MATHARTWORK

#KOSEKOMA

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.

• 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

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/

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 -3 photos

16

2

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

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...