social.sokoll.com
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
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 ,
and
For a regular n -gon inscribed in a unit circle, we have
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.
http://feedproxy.google.com/~r/TheEndeavour/~3/7KhpTEfZD4s/
#johndcook #Math
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
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
The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single tweet.www.quantamagazine.org
You wouldn't believe
what happened next...
https://twitter.com/kj_cheetham/status/1149966666836656128
#math #joke
Leaves are enjoyed for their shade, autumn colors, or taste, and the arrangement of leaves on a plant is a practical way to identify a species. However, the details of how plants control their leaf arrangement have remained a persistent mystery in botany. A Japanese plant species with a peculiar leaf pattern recently revealed unexpected insight into how almost all plants control their leaf arrangement.phys.org
To multiply two numbers by hand take a few steps but it's something we're taught in school. When dealing with big numbers, really big numbers, we need to a quicker way to do things.theconversation.com
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!
#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!
#plankton #maths #dodecahedron #pentagon #mathematics #geometry #platonic #trapezium #microscopy #electronmicroscope #calcium #algae #cyanobacteria #math
Emma Haruka Iwao calculates the value of pi to 31 trillion digits, after a lifelong fascination.www.bbc.com
