Rithmatics: Part 1

Rithmatics: Part 1

Hello!  I'm rather fascinated with Rithmatics (the magic system in Brandon Sanderson's The Rithmatist) at the moment, which means you are going to be getting a series of mathy posts.  They will all be tagged with #rithmatics .  I've been encouraged to add the cfsbf tag.  If this bothers anyone, please let me know.

In this first post we explore how all of the binding patterns for circular defenses can be derived from 9 point circles. You might be able to get everything from the pictures, but I give explanations as well.

9 Point Defenses

Let's start by talking about 9 point circles.  Start with a triangle.  Absolutely any triangle will do, but for 9 point defenses we want acute triangles (all angles less than 90 degrees) where all of the angles are distinct.  Mark the midpoints of each side and draw in the three altitudes (start at each vertex and draw the line perpendicular to the opposite side) of the triangles.  Mark the points where the altitudes intersect the sides of the triangles (there are 3 such points, one for each altitude).  Note that all of the altitudes meet a single point. Mark the midpoint of each segment connecting P to one of the vertices of the triangle.  This gives you three more points for a total of 9.  These 9 points will be distinct and lay on a circle.

Rithmatics: Part 1

This explains how to get the bind points for any 9-point defense.  However, not all defenses have 9 points.  These turn out to be very special cases of 9 point triangles where some of the points coincide.  

6 Point Defenses

To get 6 points, start with an equilateral triangle.  Any time two angles of a triangle have the same measure, the altitude from the third angle will bisect its opposite side.  Since all of the angles are the same here, all of the altitudes bisect their opposing sides.  This gives us a "9-point" circle with 6 evenly spaced points.

Rithmatics: Part 1

4 Point Defenses

This time we want an isosceles right triangle (you might know it better as a 45-45-90 triangle).  In right triangles, the legs are also altitudes, which means that the vertex at the right angle is also the point where the altitudes intersect each other. It is also the point where each leg "intersects" the other and the "half way point" between the intersection of the altitudes and itself, so it counts as 3 of the 9 points.  The resulting 4 points form a square and so are evenly spaced around the circle.

Rithmatics: Part 1

2 Point Defenses

This is the strangest case.  Here our triangle is degenerate - one of the sides has length 0, which means that the "triangle" is just a line.  To see how to follow the 9 point construction in this case, we can look at a limit.  Start with a really skinny isosceles triangle.  If you follow the construction, you get three points grouped near each approximately half way up the triangle.  The other 6 points are clustered down near the narrow base.  Now pretend the narrow point is a hinge and slowly close it. As you do, the three points in the middle get closer and closer together, the base gets narrower and narrower and the 6 points near it get closer and closer together.  In the limit this gives us a line segment and a circle which uses half of the line segment as a diameter

Rithmatics: Part 1

More Posts from Kalynaanne and Others

7 years ago

For your consideration: Adolin, Evi, and Fashion

Consider: Evi moving from Rira to Alethkar and learning to cope with the new culture and all of the safehand nonsense. Then marrying the blackthorn and collecting and analyzing fashion folios to figure out how she can be a Good Vorin Wife while still trying to be true to herself.

Consider:  Smol Adolin sitting with her, only half understanding, as she talks half to him and half to herself about balancing traditions and current fashion. And then when he shows interest - because if mom cares then so should he - she starts also getting the fashion folios for boys and young men and altering Adolin's clothes with ideas he likes from the folios.

Consider: Evi encouraging Adolin when he starts fashioning himself play armor out of the rockbud shells he finds laying around. Evi teaching smol Adolin knots and the very basics of sewing.

Consider: An older Adolin trying to follow his father’s example and getting into dueling. Adolin coming home with tears in his clothes from roughhousing and fighting his friends/rivals and Evi sitting him down and teaching him how to mend his clothes. Not just how to mend them, but how to do it in ways that make the mending look intentional and fashionable.

Consider: Evi at the war camps feeling like she is losing control of everything and her life is falling apart, but still making sure she is put together and trying to make sure her boy has his jacket because that's one of the few things she CAN still control .

Consider: After Evi’s death, Adolin seeking out the folios himself and growing closer to his tailor while he continues to improve his sewing skills because it's a connection he has to his mom that he doesn't want to lose.

Consider: Adolin taking the group to his tailor, not just because he is into fashion but because she filled something of a surrogate mother role for him after Evi died and he truly does trust her completely. And THEN in Shadesmar when he is feeling useless and helpless on the ship he sits down and sews himself a halfway decent outfit because, storm it, even if he can't control anything else, he can still control THIS and the process of the sewing reminds him of his mother's strength even when she felt helpless and that helps him keep holding himself together and doing what he can.


Tags
4 years ago

So I saw @ultimateinferno theorizing about this, and I want spoilers hidden under a cut on my blog, so I’m making a new post rather than reblogging to add to his excellent theory/meta. There are *major Rhythm of War spoilers* mixed with theorizing under the cut.

Ultimateinferno makes a good argument that Lift is the one who is eventually going to deal with Taravangian!Odium. This is *perfect*.

Lift’s “I don’t want to ever change.” You know what? If she kills Taravangian she’s going to get the opportunity to absorb Odium and ascend. Either her boon is going to give her the strength to resist taking the power so that she can deal with it some other way (maybe she could team up with Rysn??? I wonder what kind of affect shattering Odium would have...) OR she *will* take the power, but because of Cultivation’s boon it won’t affect her ability to think clearly.    

Heh, although, Lift, as she is right now, but with the power of a shard might be a whole different kind of problem. As Yanagawn points out, “She often does what she isn’t supposed to.”


Tags
3 years ago
The Brooklyn Public Library is giving eCards to teens nationwide to challenge book bans.
Literary Hub
Like we needed another reason to love libraries: with book bans ramping up in school systems around the country, the Brooklyn Public Library

Right now, and for a “limited time,” anyone in the United States between the age of 13 and 21 can apply for a free Brooklyn Public Library eCard, which gives access to 350,000 eBooks, 200,000 audiobooks, and online databases.

Teens who want to apply for the free eCard can send an email to BooksUnbanned@bklynlibrary.org or a message to @bklynfuture on Instagram.


Tags
psa
10 years ago

Shallan's Journey: Chapter 2, In Which Shallan Meets a Fire Chicken

A sudden whooshing sound made Shallan spin around and her jaw fall open in shock at the resulting vision. A burst of flame quickly resolved itself into a person and the most brilliant chicken she had ever seen! After a few moments, during which she and the new man studied each other, Pattern drifted into her view and buzzed “Shallan. Your mouth. You are staring.”

Her jaw snapped shut and she quickly looked down as she began thinking frantically. This new man was certainly pale enough to be Shin, but he had far, far too much hair and she had never heard of Shin being able to travel in fire. For that matter she had never heard of anyone being able to travel in fire. Oh storms! She had no idea what was going on or what she should do next... but... but she had gotten through unfamiliar situations before... she just had to decide how to play this. Surely it wouldn't be worse than her first few meetings with the Ghostbloods. She closed her eyes and took a deep breath to center herself. Confidence. She could do this. Pattern's gentle buzzing as he floated near her head was reassuring. He was often good at helping her sort through things and if everything went completely storms up she would at least be able to defend herself. She held her sketchbook close to her chest with her sleeved safehand and her traveling bag to her side with her freehand as she looked back up at the man and the fire chicken with what she hoped was an expression of wary confidence.

She realized that he seemed to be just as curious about her as she was about him. Well, she supposed that if he was typical of the people here, then she probably appeared quite unusual. His sparkling purple dress thing was nothing like men would wear anywhere on Roshar.

Dumbledore wasn't accustomed to being speechless, but he truly wasn't sure how to react to the young woman he found when he arrived. She seemed startled, so he kept his face serene as he stood quietly to give her time to compose herself – and him time to try to make sense of the situation. She was wearing a style of dress he had never encountered despite his many years and extensive travels and seemed to be accompanied by a small whirling mass of black lines. Most curious indeed. When she looked back up and didn't seem inclined to either attack or run away, he took a step toward her and gestured in greeting.

“My dear girl. I noticed unexpected activity here at Stonehenge and came to investigate. Would you mind telling me who you are?”

Shallan looked back at him in confusion. His language was unlike anything she had ever heard before. She opened her mouth planning to say something formal and productive, but what came out was “Who on Roshar are you and where are we?” Pattern buzzed in a way that sounded almost like a snicker. “Mmmm...There's my Shallan. The strange man probably can't understand us anymore than we can understand him.” Shallan glared at Pattern.

Dumbledore's eyes widened as he watched this exchange. She spoke a rather curious sounding language and her friend seemed to be able to communicate directly with her. This was most unusual. He began contemplating how he could communicate with her. There were spells to ease translation, but they all required the caster to have some knowledge of both of the languages they were working with, a condition he usually easily met. They would not work here though.

Shallan narrowed her eyes in thought. She had no idea how to get back to Roshar (it was clear by now that she was no longer there) and as a Lightweaver she was fairly certain her surges wouldn't be particularly helpful for getting back. As much as she didn't like it, this most likely meant that she was stuck here until Jasnah figured out what had happened and was able to rescue her. Unless Jasnah showed up soon, it wouldn't be practical for her to just sit here waiting for her. This meant that, at the very least, she needed information. Right now her best hope of information was this strange man. Shallan made eye contact with him and then pointed to herself. “Shallan.”

The man smiled and nodded to her as he repeated, “Shallan,” and responded with a similar gesture and “Albus.”

Shallan nodded slightly, “Albus.” Now what... Shallan bit her lip and then sat down as she opened her sketchbook and pulled out a pen. They couldn't communicate in words, but pictures didn't have a language. Her pen flew across the page as she quickly sketched Urithiru and the portal they had been experimenting on. She sketched the palace of Jah Keved and added lines that would hopefully suggest that she was hoping to travel there. She then drew a large slash through Jah Keved and firmer lines from the portal into a solid black blob with further lines leading to a quick sketch of her current surroundings. As she finished, she stood and turned the sketchbook toward him hopefully.

Albus studied the image thoughtfully. Whoever this girl was, she had quite a talent for drawing. That quick sketch of Stonehenge was quite remarkable. He turned his attention to the rest of the picture. There was an interesting tower that she seemed to be suggesting was the starting point of her journey. Next to it seemed to be a traveling device of some sort with the indication that it was supposed to take her to the other large building. Instead it apparently took her into a void and then dumped her here. Dumbledore nodded thoughtfully and slowly pulled out his wand.

Shallan watched with fascination as the man, Albus, she reminded herself, took out an oddly uniform stick and began weaving it through the air. To her astonishment, he began to form the image of a large stone castle in the air between them. Was this man another Lightweaver?! Was that stick some strange fabrial? The image zoomed into a room where there was an image of Albus sitting at a desk... Shallan squinted, was he...writing? The image man then looked up and over at a small image of the fire chicken. The fire chicken image flew to the image of the man, which appeared to grab the fire chicken's tail before they both disappeared in a flash of fire. Albus waved his arm and the castle also vanished.

He then wove an image of what appeared to be a home with several other people around and then added an image of himself, the fire chicken and...and Shallan... appearing in a burst of flame.

Shallan frowned. Aside from questioning the brilliance of going anywhere in a strange land with a strange man she had just met, Shallan was worried about what would happen if Jasnah made it here and she wasn't nearby. She turned back to her sketchbook and flipped to the next page. This time she started with an image of Jasnah next to an image of Urithiru with her hand up to her eyes as though looking out of the page. She followed it with an increasingly hasty series of places around Roshar with a flowing line connecting all of them in sequence. Then a picture of Jasnah at a desk surrounded by books and finally an image of Jasnah at in their current location looking sad and confused.

Albus nodded slowly. Shallan seemed to be indicating that someone would be frantically looking for her and didn't want to miss them when, if, they made it here. While he was contemplating the problem Shallan turned to Pattern. “Do you know of any way we could leave a message here for Jasnah? Maybe in Shadesmar?”

“Mmmmm... Jasnah will be tracking you, not just your path. Moving around shouldn't interfere much.”

“You are sure?”

“Nothing is sure. Sure is truth, but truth is based on lies and always changing.”

Shallan rolled her eyes. Someday she would learn not to try to get a straight answer out of Pattern. “Do you think we should go with the man and his fire chicken?”

“Mmmm... he makes good lies. ”

Right. That would be what Pattern focused on. Well, Albus had been reasonable so far and she didn't exactly have any other options. Now, how to tell him that she was willing (or at least had resigned herself) to go with him...

Shallan turned back to her sketchbook and made a sketch of the fire chicken with both her and Albus holding its tail and then got Albus's attention. He gave her a questioning look and pointed back at her Jasnah sketch montage. Shallan shrugged and pointed at Pattern. There was no point in trying to explain her rough understanding of what Pattern had tried to tell her. Albus smiled, nodded and looked around carefully to make sure they were alone before saying slowly and carefully, “The headquarters of the Order of the Phoenix may be found at number twelve, Grimmauld Place, London.”

Shallan raised her eyebrows and cocked her head. Was she supposed to have gotten anything from that? Albus sighed and repeated the first word, “The,” and then gestured to her. Shallan repeated it back to him. They went through the whole phrase that way, first with the individual words and then with subphrases until Shallan was able to repeat the whole thing back to him. The words felt strange in her mouth and she had no idea what they meant or what their importance was, but she could say them.

Fawkes, who had been flying a sort of dance in and about the standing stones, now flew over to them and dangled his tail feathers between them. Shallan held out her arm and, to Dumbledore's astonishment, her friend seemed to meld into the sleeve of her dress. This girl came with no end of surprises. Shallan took a deep breath and confidently but gently took hold of Fawkes's tail with her freehand. Dumbledore joined her and they vanished in a flash of flame.

After the events of the last year, Shallan thought she had about had her share of new, unsettling experiences. The process of traveling by fire chicken wasn't actually that shocking – she felt a little warm and a slight tickling before suddenly arriving in a dark gloomy hallway – except for the simple fact that it had happened. Shallan had accepted the fact that there were fully sentient spren. She had, very reluctantly, accepted that she was on track to become one of the new Knights Radiant – the order whose previous incarnation had betrayed all of mankind on the Day of Recreance. She knew that Jasnah could use Shadesmar to travel quickly around Roshar and that Kaladin, that storming obnoxious but fascinating bridgeman captain, could use stormlight to fly.

If the fire chicken had been a spren, she might have been able to just accept that Albus had some unknown surge that let them use fire to travel. The chicken, however, was clearly not a spren. It was a chicken. A flashy, brightly colored, singing chicken, but it was a chicken. Chickens did not travel in fire. If chickens and fire went together they became food.

While Shallan was still mostly out of it as she tried to come to terms with the idea of traveling by fire chicken, Albus gently led her down the hall to a staircase and then down into what appeared to be a kitchen. The sound of several people talking over each other startled Shallan out of her confusion just in time to notice a woman wearing short sleeves with both hands and arms exposed standing at what seemed to be a stove. She scanned the room and saw that there were boys, girls, men and women sitting together at the table eating the same food. She groaned, took a step back so that she was against the wall next to the stairs they had just come down, slid to the floor and buried her head in her arms. Oh storms. This world was nothing like Jah Keved, Kharbranth, or Alethkar.  


Tags
10 years ago
I Used Fallenwithstyle's Chart To Knit Myself A Pattern Hat! The Brown Is KnitPicks City Tweed DK And

I used fallenwithstyle's chart to knit myself a Pattern hat! The brown is KnitPicks City Tweed DK and the purple is KnitPicks Wool of the Andes sport. They were both sitting in my stash of yarn waiting to be right for something. I need to work on my consistency with keeping the floats loose enough in stranded knitting, but it isn't bad enough to be a problem.The hat also came out slightly longer than I usually prefer, but I'm super happy with it anyway :-). While I was knitting it, it occurred to me that there is potential for an amazing Pattern hat done with cables rather than colorwork. I'm not sure when I will get to it, but designing that pattern has gone in my "projects I will get to at some point" file. 

Sprenhead!

Sprenhead!

Here’s my finished Pattern hat! I’m really happy with how it came out not just as fanart but as a hat in general (and I said I didn’t need any more hats…).

I changed the chart sightly from the original version I posted, so here is the final version (it doesn’t include instructions for the flared brim or picot hem though, just the colorwork). 

Sprenhead!

Tags
10 years ago

(Probably Crazy) Nightblood Theory

So, I just had a probably crazy idea.  

What if Nightblood isn't actually completely native to Nalthis? What if Nale is bringing it back home when he gives it to Szeth? Nightblood could have been a Rosharian Shardblade (Szeth doesn't seem to question it being a shardblade) that ended up on Nalthis. Then when Vashar and Shashara awakened it, the process roused the dead/trapped spren in the shardblade.  From what we have seen,  spren require an active bond with a human to remain sentient in the physical realm.  Awakening would interact strangely with this resulting in the spren needing a steady supply of breath to remain active.  This could provide an explanation for why it sucks the breath out of people (something that is never really explained in Warbreaker). 

Nightblood's inability to fully understand what evil is and place it in a human context runs reasonably parallel to Pattern and Syl's attempts to understand the more abstract concepts of the human world.  In Nightblood's case, the spren is still trapped in the sword and since it doesn't have a proper bond with a person, it is even harder for it to learn, so it can't progress as well or as quickly as Pattern and Syl.

The more I think about this the better it is working...


Tags
3 years ago

This feels like a crazy long shot, but do I know anyone who plays Pokemon Go in the Uxie region?

2 years ago

PSA: Brandon Sanderson is holding a T-shirt design contest for the release of The Lost Metal. 

There are 3 design prompts to choose from:

*  Wayne’s Haberdashery 

* Take anything from the books and give us an Art-Deco design 

* An in-world product (you can also make up your own in-world product for Mistborn)

More details on Sanderson’s site at: https://www.brandonsanderson.com/design-contest/


Tags
10 years ago

Spy Girls

Shallan:  Daughter of rural minor noble family who goes on a journey and ends up in the court of the current political center of her world where she is slightly overwhelmed by everything and is trying to figure out how to save her family.  In the process, she discovers a plot of some sort in the underworld of the society and create and alter-ego to infiltrate it.

Vin: Daughter of the underworld who finds herself in a new crew where the rules aren't quite what they used to be and she has to adapt as they plot to completely overthrow society. As part of this, she creates an alter-ego in which she infiltrates the court as a daughter of a rural minor noble family who is here to further her family's interests.  

These girls are like two sides of the same fantastic coin and there are two things I really want to read:

1) Shallan and Vin curled up with coffee or tea or something trading infiltration stories and tips with Pattern providing commentary.

2) A scenario where these two are moving in the same court and are initially on opposite sides and they start getting suspicious of each other and eventually one confronts the other (I can't decide which way).  After talking they discover that there is more going on than either realized and essentially end up forming their own faction.


Tags
Loading...
End of content
No more pages to load
  • pokegeek151
    pokegeek151 reblogged this · 1 month ago
  • pokegeek151
    pokegeek151 liked this · 1 month ago
  • joel-saxon
    joel-saxon reblogged this · 1 month ago
  • theironseaweed
    theironseaweed liked this · 2 years ago
  • steelheartthecoinshot
    steelheartthecoinshot reblogged this · 2 years ago
  • steelheartthecoinshot
    steelheartthecoinshot liked this · 2 years ago
  • caiminnent
    caiminnent liked this · 6 years ago
  • miserycollections
    miserycollections liked this · 6 years ago
  • rhetoricandlogic
    rhetoricandlogic reblogged this · 6 years ago
  • dizzmaster02
    dizzmaster02 reblogged this · 6 years ago
  • dizzmaster02
    dizzmaster02 liked this · 6 years ago
  • jesters-armed
    jesters-armed liked this · 6 years ago
  • loud-n
    loud-n reblogged this · 6 years ago
  • loud-n
    loud-n liked this · 6 years ago
  • yourgracekate
    yourgracekate liked this · 6 years ago
  • st753m
    st753m liked this · 6 years ago
  • azfirith
    azfirith reblogged this · 6 years ago
  • azfirith
    azfirith liked this · 6 years ago
  • peachdoxie
    peachdoxie liked this · 6 years ago
  • whyisthislife
    whyisthislife liked this · 6 years ago
  • cosmerearchive
    cosmerearchive reblogged this · 6 years ago
  • cosmerearchive
    cosmerearchive liked this · 6 years ago
  • cryokina
    cryokina liked this · 6 years ago
  • kindleln
    kindleln liked this · 6 years ago
  • strandtasche
    strandtasche liked this · 6 years ago
  • usernamesaresohardimconflicted
    usernamesaresohardimconflicted liked this · 6 years ago
  • eldritchsandwich
    eldritchsandwich liked this · 6 years ago
  • muses-and-motivators
    muses-and-motivators liked this · 6 years ago
  • onlycosmere
    onlycosmere reblogged this · 6 years ago
  • onlycosmere
    onlycosmere liked this · 6 years ago
  • acimnor
    acimnor liked this · 8 years ago
  • kyra326
    kyra326 reblogged this · 8 years ago
  • pinkpuffballdude
    pinkpuffballdude liked this · 8 years ago
  • george-oswald-dannyson
    george-oswald-dannyson reblogged this · 8 years ago
  • filingrunesforfun
    filingrunesforfun liked this · 8 years ago
  • rithmaman-blog
    rithmaman-blog liked this · 9 years ago
  • shichigatsu-no-shoujou
    shichigatsu-no-shoujou liked this · 9 years ago
  • malfuria
    malfuria reblogged this · 9 years ago
  • freethinkernightseeker
    freethinkernightseeker reblogged this · 10 years ago
  • taisharnumenore
    taisharnumenore reblogged this · 10 years ago
  • taisharnumenore
    taisharnumenore liked this · 10 years ago
  • omnia-fortunae-commito
    omnia-fortunae-commito liked this · 10 years ago
  • berah-ronah
    berah-ronah liked this · 10 years ago
  • nonbinaryfrillish
    nonbinaryfrillish reblogged this · 10 years ago
  • kalynaanne
    kalynaanne reblogged this · 10 years ago
kalynaanne - Thoughts and Creations
Thoughts and Creations

So. I found my way to tumblr when I first discovered Brandon Sanderson's books. As a result, this, my main, was all Sanderson all the time. Tumblr won't let us change which blog is the main blog and my brain won't let me make this blog more general, so you'll find my general tumbling (currently including a great deal of Imperial Radch and Murderbot) on my "side blog" RithmatistKalyna.tumblr.com .

111 posts

Explore Tumblr Blog
Search Through Tumblr Tags