MOAR CHALKLINGS

Your questions got me thinking and realizing that I have additional questions:

Szeth is likely going to summon his spren as a sword eventually. Is it going to make Nightblood jealous? Will they see it as a way to destroy twice as much evil? Szeth dual wielding blades? Or Nightblood getting frustrated because Szeth really needs a long spear for a sky battle right now and he is using the sprenspear instead of a sword?

Or, would Szeth summon his spren as a shield while using Nightblood as a sword?

What is the conversation going to be like when Nightblood and the spren talk?

Or, y’all, Szeth and Nightblood and the spren in a sort of threeway poly nahel bond. Maybe the bond could dampen the spiritual cracks in Nightblood so that they don’t automatically suck all of the investiture out of anyone holding them? 

I wonder what it’s like to be Szeth’s spren.  Like, the only thing they have to do is stick close enough that he can surgebind.  Nightblood takes care of everything else.  Did some Highspren just go: “This is gonna be the easiest assignment ever heck yeah” and then sleep through the rest of the book?  Are they annoyed at not having anything to do?  Were they tired of working with more conventional Skybreakers?  What do they think of Szeth siding with Dalinar over Nale?

I have questions guys

Ohhh... this looks like fun...

Cinderella's fairy godmother is a lightweaver who sent her spren to the ball with Cinderella to maintain the illusion.  The midnight curfew is there because she could only infuse her spren with so much stormlight and the illusion will fail when it runs out.  Maybe the spren stays with the glass slipper and uses the little bit of stormlight it still has to continue maintaining just that part of the illusion...

Princess and the Pea is an easy one, relatively speaking. The princess in question is a tin-compounding Twinborn who got stuck in a touch loop at an early age. The easiest way I can think of for that to work is that she doesn’t know she’s doing it - perhaps she fundamentally doesn’t understand...

Badger and I were contemplating what color axehounds should be and then they said there should be sparkle axehounds and that reminded me of My Little Pony and then Badger drew this and it is EXCELLENT. 

my little axehound, my little axehound ~

Rithmatics: Part 6, 9 Point Conics and Triangle Centers

Note: From this point on we are drifting farther and farther from what we know from the book. The math is all solid, but its application to Rithmatics is much more speculative.

In rithmatics, the 9-point circle plays an important role in constructing lines of warding and identifying bind points.  We also know that there exist elliptical lines of warding and that they "only have two bind points."  Now, in math we are frequently told things like "You can't take a square root of a negative number", which are true in the given system (real numbers) but not true in general.  The construction for the 9-point circle, as described in the book, doesn't work for ellipses.  However, there is a generalized 9-point conic construction.  To understand it, we need to start with a little bit of terminology.

A complete quadrangle is a collection of 4 points and the 6 lines that can be formed from them.  For our purposes, we will be concerned with complete quadrangles formed from the vertices of the triangle and a point inside the triangle.  The 6 lines are then the sides of the triangles and the three lines connecting the center point to the vertices.

The diagonal points of a complete quadrangle are the three intersection points formed by extending opposite sides of the quadrangle.  If we have a triangle ABC with center P, then the intersection of AB with PC is a  diagonal point.

If you take the midpoints of the 6 sides of a complete quadrangle and the 3 diagonal points of that quadrangle, these 9 points will always lie on a conic. This conic is the 9-point conic associated with the complete quadrangle.

Note that if we choose our point in the center of the triangle to be the point where the altitudes meet (known as the orthocenter), then this construction is exactly what we have been doing to create 9-point circles.

There are four classical and easily constructable triangle centers - the orthocenter, circumcenter, centroid, and the incenter.  There are over 5000 other possible notions of the center of a triangle, but most of them cannot be easily geometrically constructed and they get increasingly complicated. 

Let's look at each of these 4 triangle centers and the conic they produce for a particular triangle. We will use a 40-60-80 triangle in each case for illustration purposes, but the results will be very similar for any acute triangle with 3 distinct angles.

Orthocenter: We already know about the orthocenter (that is what most of this series has been focused on so far).  For reference, here is what the 9-point circle for this triangle looks like:

Circumcenter: The circumcenter of a triangle is found by finding the midpoint of each side of the triangle and drawing in the perpendicular bisectors.  The points where the perpendicular bisectors meet is the circumcenter.  Note: This point is also the center of the circle that can be circumscribed around the triangle.

Unlike with the orthocenter, the lines we use to construct the circumcenter (the dashed lines in the diagram) are not part of the complete quadrangle, so we have to finish the quadrangle after we have identified the circumcenter.  The resulting conic is an ellipse.

Centroid: The centroid of a triangle is formed by finding the midpoint of each side of the triangle and connecting it to the opposite vertex.  The intersection of these median lines is the centroid.

The lines used to construct the centroid are part of the complete quadrangle, but we have the interesting situation where the centers of each side are also the diagonal points of the complete quadrangle.  This means that, regardless of the triangle used, we will only ever have 6 distinct points.  The resulting conic is an ellipse that is tangent to all three sides of the triangle.

Incenter: The incenter of a triangle is the intersection of the  angle bisectors of the triangle.  

Note that the lines used to construct the incenter of the triangle are also the additional lines of the complete quadrangle.  In addition, as long as the angles of the original triangle are distinct, the 9 points in the construction will all be distinct.  The resulting conic is an ellipse.

In Summary:  There are lots of ways that we could potentially construct a 9-point ellipse from a triangle.  Of these options, I would guess that the construction using the  incenter of the triangle is the most likely to produce valid rithmatic structures.  I lean this way because, as with the orthocenter, constructing the incenter also constructs the complete quadrangle and its diagonal points.  Furthermore, the 9 points of the construction will all be distinct (except in special cases). As such, we will explore 9-point ellipses constructed with the incenter more thoroughly in the next post. 

Last Chance to Pledge for Full Negative Book

Friends. Readers. Fellow nerds with impeccable taste. We are officially in the home stretch. The final 24 hours. The last lap. The dramatic climax of the movie where everything explodes in slow motion and the music swells and someone says something heroic right before punching a fascist in the face. (Okay, that last bit’s just wishful thinking, but after the week we’ve all had, I think we…

Last Chance to Pledge for Full Negative Book

V is for Vinebud

GUYS.  Ben McSweeney was also at the Atlanta Brandon Sanderson signing!  And was impressed enough with my notebook of rithmatics that he DREW ME A PICTURE!!!!

If you have questions about editing or the Coppermind in general, I would also be happy to help/encourage you :-) 

In the vein of wikipedia’s wikiprojects, I have recently made a few pages which will help people who are looking for a way to contribute to the coppermind but don’t know where to look to find things that need doing. They are a set of pages which list the status of various articles, so you can see which articles really need help. As a new contributor, adding content to the articles in the good or stub categories of your favorite series would be a reasonable place to start.

Alcatraz

Cosmere wide

Elantris & The Emperor’s Soul

Legion

Mistborn: Trilogy, Wax & Wayne, Crafty RPG

The Reckoners

Rithmatist

The Stormlight Archive (warning: this page is huge, there’s just so many articles relating to it it’s still not very usable)

Warbreaker

For more details on what the various categories mean, jump under the cut.

Read More

My thought process on reading this:

Yeeesssss sibling interatctions!  

Mmm, if Lift were Kaladin's little sis, she would be the little sis of all of Bridge 4.  Since Rock is in charge of food, he would be her favorite big bro (or maybe uncle?...hmmm...either way works) and she would hang out around him and try to snitch food constantly.  Rock can see Wyndle and they conspire to try to keep her somewhat in line, but Rock is also never actually mad about her eating.   Sigzil takes it on himself to be her tutor and both starts teaching her to read glyphs and helping her understand her awesomeness by experimenting with it.  Lift isn't thrilled with his tutoring and sneaks off whenever she can. She learns much more about her awesomeness from the games she gets into with Lopen.  She catches Lopen glowing sometime and insists (with much stomping and pouting that isn't actually necessary because Lopen doesn't really need convincing) that he teacher her how to glow because that is so awesome!  At some point he sticks her to the wall and starts to laugh at her but then she becomes awesome and slides down the wall and past him making the bottoms of his shoes awesome as she goes past so that when he tries to turn around he slips and falls.  Lopen is briefly stunned and then bursts out laughing and congratulates her and from then on they are constantly trying to use their powers to get one over on each other.

http://therustyrobot.tumblr.com/post/102898558995/does-anyone-else-really-want-to-see-the-dynamic

does anyone else really want to see the dynamic between kaladin and lift

because I’ve been thinking about it all day and I feel like since most of the radiants so far are pretty tall and lift is. not. she’d want to see what all the tall people were doing so since kaladin’s the tallest she’d end...

I'm slightly late, but here you go!  Have a little story :-)

Adolin's first reaction was to stare blankly at her. After what felt like ages, he shook himself and asked slowly, “I...don't think I heard you right...could you say that again?”

Shallan rolled her eyes, “I want to find a way to actually watch and document the highstorms.”

He took a deep breath. “Ok. That's what I thought you said... Why?! Wasn't being stuck out in one in the chasms enough?”

She laughed, “Nope – it just made me realize how much we don't know.”

"Of course it did." Adolin groaned. “If I don't help you with this, you're just going to find a way on your own, aren't you?” He sighed. “Fine. At least this way I'll know what's going on. Knowing you, you already have at least half of a plan. Let's hear it.”