Category: Taylor

fuckyeahphysica: If one remembers this partic…

fuckyeahphysica:

If one remembers this particular episode from the popular sitcom ‘Friends’ where Ross is trying to carry a sofa to his apartment, it seems that moving a sofa up the stairs is ridiculously hard.

But life shouldn’t be that hard now should it?

The mathematician Leo Moser posed in 1966 the following curious mathematical problem: what
is the shape of largest area in the plane that can be moved around a
right-angled corner in a two-dimensional hallway of width 1?
This question became known as the moving sofa problem, and is still unsolved fifty years after it was first asked.

image

The most common shape to move around a tight right angled corner is a square.

And another common shape that would satisfy this criterion is a semi-circle.

image

But
what is the largest area that can be moved around?

Well, it has been
conjectured that the shape with the largest area that one can move around a corner is known as “Gerver’s
sofa”. And it looks like so:

image

Wait.. Hang on a second

This
sofa would only be effective for right handed turns. One can clearly
see that if we have to turn left somewhere we would be kind of in a tough
spot.

Prof.Romik from the University of California, Davis has
proposed this shape popularly know as Romik’s ambidextrous sofa that
solves this problem.

image

Although Prof.Romik’s sofa may/may not be the not the optimal solution, it is definitely is a breakthrough since this can pave the way for more complex ideas in mathematical analysis and more importantly sofa design.

image

Have a good one!

Photo

Photo

asapscience: Mathematicians finally cracked L…

asapscience:

Mathematicians finally cracked László Fejes Tóth’s zone conjecture, a 44-year-old geometry problem! Learn about it here: http://bit.ly/2Cxqp0C

[#Einsteinsmama]

mathblab: Koch Snowflake: Finite area, Infinit…

mathblab:

Koch Snowflake: Finite area, Infinite perimeter.

The Koch Snowflake has finite area but infinite perimeter… yeah that happens with fractals. This abstract curve requires an infinite process (depicted in the gif) to construct and is an example of a fractal–a mathematical set (usually a curve or geometric figure) which exhibits a repeating pattern that displays at every scale. (More about fractals here https://en.wikipedia.org/wiki/Fractal)

But How? It seems clear that the area would be finite since the figure encloses a finite amount of space. To grasp why the Koch Snowflake has infinite perimeter, notice how as the iterations progress, the edges become more and more intricate. Now imagine trying to draw the edges with a pen. Since the construction of the snowflake continues indefinitely, the edges become infinitely intricate and you could never finish detailing these intricacies with your pen (that is the intuitive argument at least. I’ll leave the precise calculations up to you).

Fractals may seem so abstract and impractical but they actually have many useful real-world applications. For example, Benoit Mandelbrot (considered the “father of fractals”) found that stock market prices could be modeled with a factual curve. Check the wiki page for a long and diverse list of applications.

Fractal geometry may seem more abstract than traditional geometry but Mandelbrot argues that fractals are “the geometry of nature”. Objects in nature have random irregularities and are seemingly infinite in their intricacies. Attempting to incorporate this in drawings or animations is extremely difficult. Movie special effects and CGI often use fractals to make objects appear more natural looking. Since fractals can be made with mathematical formulae they are easy to generate with a computer. The first Star Wars movies were renowned for their special effects and were some of the first to use fractals to generate life-like explosions and landscapes of other worlds.

picturesquephysics: A Canadian Mathematical Olympiad training…

picturesquephysics:

A Canadian Mathematical Olympiad training question. 

6 was scared of 7 because 7, 8 ,9 but why did 7 eat 9?

simonein2015:
reallyfunnyshortjokes:
Because you’re supposed to eat 3 squared meals a day.
this is…

macleod: this fibonacci joke is as bad as the last two you heard combined

macleod:
this fibonacci joke is as bad as the last two you heard combined

PSA: How to write a blackboard bold Z

thousandmaths:
You know what doesn’t actually matter but always bothers me? This:
No.
Stop.
Today…

coolmathstuff: justsomeantifas: yall wanna hear something cool and completely unrelated to this…

coolmathstuff:

justsomeantifas:
yall wanna hear something cool and completely unrelated to this…

mathblab: From the 1955 College Entrance Examination Board’s…

:

From the 1955 College Entrance Examination Board’s report on the Commission on Mathematics.