social.sokoll.com

Search

Items tagged with: math

Mathematicians Discover the Perfect Way to Multiply | WIRED

Normal multiplication we learn in school requires n².
Now they found an Algorithm that can do it in n x log n

#math #science
 
Bild/Foto
A #brachistochrone #curve is the curve of fastest descent between two points not directly below each other -- interestingly not a straight or polygonal line but a cycloid.

#math #physics
 
Bild/Foto
A #brachistochrone #curve is the curve of fastest descent between two points not directly below each other -- interestingly not a straight or polygonal line but a cycloid.

#math #physics
 

Eye of the Universe - Mandelbrot Fractal Zoom (e1091) (4k 60fps) - YouTube


The beauty of #math
#Mandelbrot #fractals

 

Ratio of area to perimeter


Given a curve of a fixed length, how do you maximize the area inside? This is
known as the isoperimetric problem.

The answer is to use a circle. The solution was known long before it was
possible to prove; proving that the circle is optimal is surprisingly
difficult. I won't give a proof here, but I'll give an illustration.

Consider a regular polygons inscribed in a circle. What happens to the ratio
of area to perimeter as the number of sides increases? You might suspect that
the ratio increases with the number of sides, because the polygon is becoming
more like a circle. This turns out to be correct, and it's not that hard to be
precise about what the ratio is as a function of the number of sides.

For a regular polygon inscribed in a circle of radius r ,

Bild/Foto

and

Bild/Foto

For a regular n -gon inscribed in a unit circle, we have

Bild/Foto

We used the double-angle identity for
sine in the second line above.

As n increases, the ratio increases toward 1/2, the ratio of the area of a
unit circle to its circumference.

Here's a plot of the ratios as a function of the number of sides.

Bild/Foto

Bild/Foto

http://feedproxy.google.com/~r/TheEndeavour/~3/7KhpTEfZD4s/
#johndcook #Math
Ratio of area to perimeter

John D. Cook: Illustrating isoperimetic problem with regular polygons

 

Ratio of area to perimeter


Given a curve of a fixed length, how do you maximize the area inside? This is
known as the isoperimetric problem.

The answer is to use a circle. The solution was known long before it was
possible to prove; proving that the circle is optimal is surprisingly
difficult. I won't give a proof here, but I'll give an illustration.

Consider a regular polygons inscribed in a circle. What happens to the ratio
of area to perimeter as the number of sides increases? You might suspect that
the ratio increases with the number of sides, because the polygon is becoming
more like a circle. This turns out to be correct, and it's not that hard to be
precise about what the ratio is as a function of the number of sides.

For a regular polygon inscribed in a circle of radius r ,

Bild/Foto

and

Bild/Foto

For a regular n -gon inscribed in a unit circle, we have

Bild/Foto

We used the double-angle identity for
sine in the second line above.

As n increases, the ratio increases toward 1/2, the ratio of the area of a
unit circle to its circumference.

Here's a plot of the ratios as a function of the number of sides.

Bild/Foto

Bild/Foto

http://feedproxy.google.com/~r/TheEndeavour/~3/7KhpTEfZD4s/
#johndcook #Math
Ratio of area to perimeter

John D. Cook: Illustrating isoperimetic problem with regular polygons

 

Enrico Ronchi auf Twitter: "Even if you do not speak Italian, look at how an Italian newspaper is explaining the #covid-19 rule of 4 m2 per shop client 🙄 What debate on #crowd science can we have in 🇮🇹 with this type of journalism? #BacktoSchool #4×4=4 😜 https://t.co/tbHEmzh1Yy" / Twitter


#Math #Italy @Andrea Borgia @Fernando Santagata

https://twitter.com/Enrico_Evac/status/1260287090824228865
 

Warum muss ich da an die Corona-Krise denken?! 🤪


https://xkcd.com/2295/

#xkcd #math #garbage #müll
 

Philosophy Matters auf Twitter: "Today’s Bad Pun, from our friends in the Euclidian Geometry Department https://t.co/hglKRP0YDj" / Twitter


Happy #punday
#math #humor

https://twitter.com/PhilosophyMttrs/status/1236902110438064129
 
Bild/Foto
Meesa suspects @Jennifer Freeman will be liking theesa post! :P

#humor #math
 
http://scienceblogs.de/mathlog/2020/02/01/der-mittelpunkt-der-welt/

#brexit #math
http://scienceblogs.de/mathlog/2020/02/01/der-mittelpunkt-der-welt/
Der Mittelpunkt der Welt
 

Physics & Astronomy Zone🔭 auf Twitter: „The Math Dance 😍 https://t.co/xBIcoY4o87“ / Twitter


#math

https://twitter.com/ZonePhysics/status/1206574036635070464
#math
 
#followerpower

I once found a site which was called_Git in layman's terms_ or similar and contained a complicated mathematical description of #git, e.g, that git is some kind of spehere or other multi dimensional #topology
Unfortunately I don't remember the sites address and no longer can find it.
Does anybody know this site?

#math #git #humor #programming #help
 

Robin Houston sur Twitter : "News! 42 is the sum of three cubes. https://t.co/0tLS8ZyhrQ 42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3"


#math #science #fun

https://twitter.com/robinhouston/status/1169877007045296128
 

Robin Houston sur Twitter : "News! 42 is the sum of three cubes. https://t.co/0tLS8ZyhrQ 42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3"


#math #science #fun

https://twitter.com/robinhouston/status/1169877007045296128
 

I asked myself that question for at least 30 years ;-)


reshare from @micha@pluspora.com

Tweet von Steffen Christensen (@Wikisteff) um 26. Aug., 04:48 Holy shit.
You can pronounce #hex numbers, people!

#hexadecimal #math
/c @hexadecim8 #Infosec #devops https://t.co/HtDmvXD9Pr

https://twitter.com/Wikisteff/status/1165818361097392128
 
Tweet von Steffen Christensen (@Wikisteff) um 26. Aug., 04:48 Holy shit.
You can pronounce #hex numbers, people!
#hexadecimal #math
/c @hexadecim8 #Infosec #devops https://t.co/HtDmvXD9Pr

https://twitter.com/Wikisteff/status/1165818361097392128

Twitter: Liz Henry on Twitter (Liz Henry)

 
Tweet von Steffen Christensen (@Wikisteff) um 26. Aug., 04:48 Holy shit.
You can pronounce #hex numbers, people!
#hexadecimal #math
/c @hexadecim8 #Infosec #devops https://t.co/HtDmvXD9Pr

https://twitter.com/Wikisteff/status/1165818361097392128

Twitter: Liz Henry on Twitter (Liz Henry)

 

Decades-Old Computer Science Conjecture Solved in Two Pages


https://www.quantamagazine.org/mathematician-solves-computer-science-conjecture-in-two-pages-20190725/

#math #science
 

You wouldn't believe

what happened next...


https://twitter.com/kj_cheetham/status/1149966666836656128
#math #joke
 

You wouldn't believe

what happened next...


https://twitter.com/kj_cheetham/status/1149966666836656128
#math #joke
 
Unusual Japanese plant inspires recalculation of equation used to model leaf arrangement patterns

This is fascinating. How different pattern are recognizable in leaves
#math #nature #plants #science
 
We've found a quicker way to multiply really big numbers

If you need to multiply trillions of numbers
#math #science
 
Apparently there is a eukaryotic phytoplankton called Braa­rudosphaera bigelowii which surrounds itself with twelve regular pentagonal CaCO3 scales (each of which in turn is constructed from five isosceles trapeziums - yes, they really are - look carefully). Each pentagon edge measures about 5μm. I am not a marine biologist so I have no idea why it does this but what a stunning piece of micro architecture it is!
Bild/Foto
#plankton #maths #dodecahedron #pentagon #mathematics #geometry #platonic #trapezium #microscopy #electronmicroscope #calcium #algae #cyanobacteria #math
 
Apparently there is a eukaryotic phytoplankton called Braa­rudosphaera bigelowii which surrounds itself with twelve regular pentagonal CaCO3 scales (each of which in turn is constructed from five isosceles trapeziums - yes, they really are - look carefully). Each pentagon edge measures about 5μm. I am not a marine biologist so I have no idea why it does this but what a stunning piece of micro architecture it is!
Bild/Foto
#plankton #maths #dodecahedron #pentagon #mathematics #geometry #platonic #trapezium #microscopy #electronmicroscope #calcium #algae #cyanobacteria #math
 
Apparently there is a eukaryotic phytoplankton called Braa­rudosphaera bigelowii which surrounds itself with twelve regular pentagonal CaCO3 scales (each of which in turn is constructed from five isosceles trapeziums - yes, they really are - look carefully). Each pentagon edge measures about 5μm. I am not a marine biologist so I have no idea why it does this but what a stunning piece of micro architecture it is!
Bild/Foto
#plankton #maths #dodecahedron #pentagon #mathematics #geometry #platonic #trapezium #microscopy #electronmicroscope #calcium #algae #cyanobacteria #math
 
@Neurosehoernchen @Jakob Dörre
https://twitter.com/gewuenschkind/status/1114129618821439488

#math #pupils
 
Hey everyone, I’m #newhere. I’m interested in #agi, #art, #math, #philosophy, #physics, #science, and #sociology.
 
Emma Haruka Iwao smashes pi world record with Google help #math #maths #science #pi
 
Later posts Earlier posts