spring-of-mathematics
asapscience:

via Reddit user cgibbard: “The first transformation is the classic hinged dissection of an equilateral triangle into a square popularised by Dudeney.
The Wallace-Bolyai-Gerwien theorem shows that any two polygons with equal area must admit a dissection into finitely many pieces where one is allowed to arbitrarily rotate and translate the pieces to go from one polygon to the other. The problem about whether a hinged dissection exists remained open until 2007. You can read the paper here, which presents a method which always works to find a hinged dissection.”


Mind blown!

asapscience:

via Reddit user cgibbard: “The first transformation is the classic hinged dissection of an equilateral triangle into a square popularised by Dudeney.

The Wallace-Bolyai-Gerwien theorem shows that any two polygons with equal area must admit a dissection into finitely many pieces where one is allowed to arbitrarily rotate and translate the pieces to go from one polygon to the other. The problem about whether a hinged dissection exists remained open until 2007. You can read the paper here, which presents a method which always works to find a hinged dissection.”

Mind blown!

doctorwho
doctorwho:

doctorwho:

30 Days of Summer Time Doctor Who
Hello, Whovians and happy summer! With all this sunshine and fun times going on, we thought to ourselves “hey, we should do a thing.”

So we figured why not start a 30 Days meme?

Each day, starting tomorrow, June 21, make a post responding to the day’s challenge. It can be text, an image, your art, a video - whatever you think works best for your answer. Post it to your blog with the tag #30 Days of Doctor Who and we’ll go through and reblog some of our favorites.

30 days is a lot of dayage, so don’t worry if you can’t do all of the days. The point is to have fun with this and be creative! 

So have at it:
Day one (21 June): Who was your first Doctor?
Day two: Who is your favorite companion, either full time or one off? 
Day three: Invent a new feature for the Sonic Screwdriver. We know it doesn’t do wood, but can it clean up spilled drinks?
Day four: Who has been your favorite historical appearance? Was it Madame de Pompadour? Maybe Winston Churchill? 
Day five: What’s your favorite episode?
Day six: If you were the Doctor, what would your catch phrase be? Ahoy, mateys? To infinity and beyond?
Day seven: Take a selfie in front of a TARDIS! It could be a poster, a toy, a drawing, anything! Just make sure to tag it with #infrontofthetardis!
Day eight: What’s your favorite Doctor Who audio adventure? If you don’t listen to the audios, click here tell us which summary you think sounds exciting!
Day nine: Which Doctor Who alumni would you like to bring back? This could be either a character or an actor, your choice! 
Day ten: What’s your favorite piece of music from the show? Did you like Vale Decem? Or perhaps Rose’s Theme?
Day eleven: Name a who-ism you use irl! Do you like to run around saying allons-y? Do you tell people not to blink?
Day twelve: Come up with a name for a Doctor Who recipe! Something like Davros donuts or Prisoner Zero pizza.
Day thirteen: Who would be your ideal Team TARDIS?
Day fourteen: Mods are asleep! Anything goes!
Day fifteen: Which regeneration of the Doctor would you most like to meet and why? 
Day sixteen: Which episode or scene made you feel all the feels?
Day seventeen: Name a crossover that you’d love to see. 
Day eighteen: The TARDIS has a near infinite number of rooms including a swimming pool, a library, and a swimming pool inside the library. Which room would you like to spend time in? 
Day nineteen: What’s your favorite Doctor Who-related youtube video? 
Day twenty: Think of the last movie you saw. Would the protagonist be a good companion? Or maybe they’d be the villain?
Day twenty-one: Name a planet that you’d like to visit in the TARDIS. Maybe you’d like to go to the planet the planet of slightly over-inflated beach balls, let us know!
Day twenty-two: What songs would appear on your Doctor Who playlist? Make us a mixtape!
Day twenty-three: What would your Time Lord name be? The Magician? The Carpenter?
Day twenty-four: Take a picture with something irl that you think could be from Doctor Who?
Day twenty-five: What’s your favorite Doctor Who art? Make sure to give the artist credit if it’s not yours!
Day twenty-six: Show us your best Doctor Who cosplay but you can only use things you can find in your closet. 
Day twenty-seven: Who is your favorite Doctor Who-related tumblr that isn’t us?
Day twenty-eight: Write an episode summary for Series 8! What do you think the Twelfth Doctor and Clara will have to face? 
Day twenty-nine: Who is your favorite Time Lord other than the Doctor? The Rani? The Master? 
Day thirty (20 July): Make a TARDIS out of things you find in your room! 

In case you missed it, we’re doing a thing!

@smallish-giraffee

doctorwho:

doctorwho:

30 Days of Summer Time Doctor Who

Hello, Whovians and happy summer! With all this sunshine and fun times going on, we thought to ourselves “hey, we should do a thing.”

So we figured why not start a 30 Days meme?

Each day, starting tomorrow, June 21, make a post responding to the day’s challenge. It can be text, an image, your art, a video - whatever you think works best for your answer. Post it to your blog with the tag #30 Days of Doctor Who and we’ll go through and reblog some of our favorites.

30 days is a lot of dayage, so don’t worry if you can’t do all of the days. The point is to have fun with this and be creative! 

So have at it:

  • Day one (21 June): Who was your first Doctor?
  • Day two: Who is your favorite companion, either full time or one off? 
  • Day three: Invent a new feature for the Sonic Screwdriver. We know it doesn’t do wood, but can it clean up spilled drinks?
  • Day four: Who has been your favorite historical appearance? Was it Madame de Pompadour? Maybe Winston Churchill? 
  • Day five: What’s your favorite episode?
  • Day six: If you were the Doctor, what would your catch phrase be? Ahoy, mateys? To infinity and beyond?
  • Day seven: Take a selfie in front of a TARDIS! It could be a poster, a toy, a drawing, anything! Just make sure to tag it with #infrontofthetardis!
  • Day eight: What’s your favorite Doctor Who audio adventure? If you don’t listen to the audios, click here tell us which summary you think sounds exciting!
  • Day nine: Which Doctor Who alumni would you like to bring back? This could be either a character or an actor, your choice! 
  • Day ten: What’s your favorite piece of music from the show? Did you like Vale Decem? Or perhaps Rose’s Theme?
  • Day eleven: Name a who-ism you use irl! Do you like to run around saying allons-y? Do you tell people not to blink?
  • Day twelve: Come up with a name for a Doctor Who recipe! Something like Davros donuts or Prisoner Zero pizza.
  • Day thirteen: Who would be your ideal Team TARDIS?
  • Day fourteen: Mods are asleep! Anything goes!
  • Day fifteen: Which regeneration of the Doctor would you most like to meet and why? 
  • Day sixteen: Which episode or scene made you feel all the feels?
  • Day seventeen: Name a crossover that you’d love to see. 
  • Day eighteen: The TARDIS has a near infinite number of rooms including a swimming pool, a library, and a swimming pool inside the library. Which room would you like to spend time in? 
  • Day nineteen: What’s your favorite Doctor Who-related youtube video? 
  • Day twenty: Think of the last movie you saw. Would the protagonist be a good companion? Or maybe they’d be the villain?
  • Day twenty-one: Name a planet that you’d like to visit in the TARDIS. Maybe you’d like to go to the planet the planet of slightly over-inflated beach balls, let us know!
  • Day twenty-two: What songs would appear on your Doctor Who playlist? Make us a mixtape!
  • Day twenty-three: What would your Time Lord name be? The Magician? The Carpenter?
  • Day twenty-four: Take a picture with something irl that you think could be from Doctor Who?
  • Day twenty-five: What’s your favorite Doctor Who art? Make sure to give the artist credit if it’s not yours!
  • Day twenty-six: Show us your best Doctor Who cosplay but you can only use things you can find in your closet. 
  • Day twenty-seven: Who is your favorite Doctor Who-related tumblr that isn’t us?
  • Day twenty-eight: Write an episode summary for Series 8! What do you think the Twelfth Doctor and Clara will have to face? 
  • Day twenty-nine: Who is your favorite Time Lord other than the Doctor? The Rani? The Master? 
  • Day thirty (20 July): Make a TARDIS out of things you find in your room! 

In case you missed it, we’re doing a thing!

@smallish-giraffee

spring-of-mathematics

spring-of-mathematics:

Sketching Sum of sine functions:

Image 1: A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue). The red dots represent the wave nodes. Harmonic waves travelling in opposite directions can be represented by the equations below:

y= Yo.sin(kx - ωt),  and y= Yo.sin(kx + ωt)

So the resultant wave y equation will be the sum of y1 and y2 .By using the trigonometric sum-to-product identity for ‘sin(u) + sin(v)’ to simplify:

 y = Yo.sin(kx - ωt) + Yo.sin(kx + ωt) = 2.Yo.cos(ωt).sin(kx)

Images 3, and 4:  A three-dimensional standing wave on a disk; this is the fundamental mode & A higher harmonic standing wave on a disk with two nodal lines crossing at the center.

Images 5:  A “standing wave” in a stream crossing a sandy beach into the sea by Jim Richardson. In physics, a standing wave is a wave that remains in a constant position. Two opposing waves combine to form a standing wave. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. (See more at: Standing Wave on Wikipedia)

Image 6: Two opposing waves combine to form a standing wave.