Mmm..  I Distinctly Don't Need More Projects Right Now, But I Can Tell You What Would Help Get Stuff

Look. One of Wit’s goals in life is to poke fun at people and make them uncomfortable. I’m choosing to believe that that is Wit’s goal here. Jasnah gets it and knows that reacting will just encourage him, so she does her best to avoid reacting outwardly and just inwardly rolls her eyes.

They get along well. They are friends. They are co-conspirators. They challenge each other. Jasnah appreciates that enough to put up with the nonsense. That’s all. 

active footage of me trying to rationalize chapter 99 in my brain

Hey Cosmere fandom, it’s book rec time.

The book series in question is the Imperial Radch Trilogy by Ann Leckie. In order, the books are Ancillary Justice, Ancillary Sword, and Ancillary Mercy.

It’s a space opera with significant focus on character and relationships. The POV character is Breq, an aro-ace space warship AI in a human body who sets out on an impossible journey to kill the Lord of the Radch (the local 3000 year old space emperor) to revenge her beloved Lieutenant. Along the way she (unintentionally and reluctantly) collects people (humans, ships, aliens,...) in a gloriously messy found family.

* It’s super queer 

* Characters actively struggle with depression, anxiety, addiction, etc.

* Almost everyone is a PoC

* For the sake of Propriety everyone wears gloves and bare hands are super scandalous. 

These books are amazing and you should strongly consider reading them. The audio book versions are also fabulous.

If you’ve already read them, I’ve been Radch posting on my other blog (RithmatistKalyna) and I would love to talk with people both about the books/characters/tea sets/etc and all of the Cosmere crossover potential.

Sanderson fans, you can get an exclusive Stormlight Archive Pocket Companion on Bookstore Day‬ April 30th! Find a participating store here.

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/

Sisters

After some thought, she decided that the concept of loving siblings was a little like the Allomantic pulse lengths she was supposed to be looking for - they were just too unfamiliar for her to understand at the moment.

Oh, Vin. Your brother may have helped you survive, but he was a horrible, horrible brother. And she HAD a baby sister that their mom killed.  I can't even...

Vin still needs to have Lift as a little sister.  Then, one night when Shallan is out on a mission as Veil she needs to come across them and bring them in off the streets and eventually be accepted into their little group as the big sister. She would try to tame them somewhat and teach them things like writing, but they would spend just as much time corrupting Shallan.  They would create an alter-ego for Lift so that the Ladies Davar, Valette and [I'm still trying to come up with a good name] could go out together, but they would also create a third alter-ego for Shallan (beacuse they wouldn't want the ghostbloods to recognize Veil) so that they could sneak out in the streets together.

Now I really want to know if burning copper affects lightweaving at all... Can Vin see through lightweaving if she is burning copper? or maybe if she is burning tin? hmmm.... Also, if Shallan weaves a disguise for another Radiant, can they maintain it with their stormlight even if they aren't a light weaver?

Alloy of Law:  make Sherlock and Watson vigilantes from the wild west and then send them to a steampunk city where they acquire a brilliant but somewhat naive badass girl apprentice.  Oh, and they all have magic.

Hey y’all, it’s Kaly reads a poem time again.  This one is called Entropy’s Embrace.  It isn’t quite a cosmere specific poem, but it is a great poem, was written by our friend worldsingers and it does have some lovely cosmere evoking imagery.  You can find the text and a review of the poem here.

Ok.  Completely new post because the other one keeps reverting to the cut off version.  This is my interpretation of Shallan's Lullaby from Words of Radiance. So far as I am aware the tune doesn't belong to anything else.

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. 

Gonna attempt Febroary, a snow lep for day 1 !