Oathbringer Speculation: Timbre

Rithmatics: Part 2, the potential for 5 point defenses

In the last post we looked at what happened with acute triangles with three distinct angles, equilateral triangles, and the isosceles right triangle.  In this post we consider non-isosceles right triangles.

The Potential for 5 Point Defenses

Let's consider what happens when we look at non-isosceles right triangles.  As with the 4 point case, the right angle vertex counts as 3 of the 9 points.  The difference here is that the altitude from the right angle vertex no longer bisects the hypotenuse, which gives us a 5th point.  The three side midpoints and the right angle vertex still form a rectangle.  It is interesting to note that the resulting circle has 3 arcs of the same length - the arcs corresponding to the short sides of the rectangle and the one connecting the short leg of the triangle to the hypotenuse.  This seems like it would be important to keep in mind when constructing defenses based on such circles.  Also note that, as with 9 point circles, there are infinitely many variations on the 5 point circle since different right triangles can lead to different bind point spacing.

In the image below I include a speculative idea I've had.  Since there are vertices which count as multiple points in the 9 point construction, it seems from a mathematical perspective like you ought to be able to bind multiple things to this point.  Whether or not this actually works rithmatically is currently unconfirmed. I will hopefully be able to find out at the upcoming Atlanta signing.

Rithmatics: Part 4, obtuse triangles

In the previous posts we have addressed all acute and right triangles.  In this post, we look at what happens if the triangle is obtuse.

Obtuse triangles and the 9-Point Circle Construction

In an obtuse triangle, two of the altitudes fall outside of the triangle. This appears to be a problem, but we can work around it.  The 9 point circle construction we have been using so far is the special case of a more general 9 point conic construction that starts with 4 points.  This more general construction produces a circle whenever the 4 points are the three vertices of a triangle and its orthocenter (the point where the three altitudes intersect).  To find the orthocenter of an obtuse triangle we have to extend the altitudes to find where they intersect outside of the triangle.  We then use the three midpoints of the sides of the triangle, the three points where the altitudes intersect the opposite side (or side extension) and the midpoints of the segments connecting the orthocenter to the three vertices of the triangle.  As you can see in the diagram below, this ends up being the same triangle you would get from considering the acute triangle formed by the orthocenter and acute vertices of the original triangle.  This means that obtuse triangles can give us a different perspective on our circles, but will not produce any new patterns we couldn't get using acute triangles.  The advanced rithmatic theorist should be aware of this but for basic rithmatics it is fine to ignore obtuse triangles.

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.”

Because Syl would be fascinated by lava lamps and try to emulate them.  Clearly.

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...

For the Blad design, wouldn't another good idea be to put stabilizing lines of forbidding between the tips of the ellipses, so they are outside the defense? They would stabilize and anchor it, not restrict movement, and also protect from incoming attacks.

That would be great, but unfortunately it won't quite work.  If you connect the tips of the ellipses, this is what will happen:

You could decrease the size of the portion that is cut off by playing with the dimensions of the ellipses, but you are never going to get the tip of the ellipse to stay inside that sharp angle at the top.  The only Line of Forbiddance that touches the bind point at the tip and doesn't intersect the rest of the ellipse is the tangent line, which would be perpendicular to the major axis and thus never reach the second ellipse.  You could contain the entire diagram in a square, but then you also can't attack.

If we could get bind points in places other than the tips, then a variation on your idea might work well.  I have ideas for how we might be able to construct elliptic defenses with more bind points, but writing that up will require more coherence than I have this time of night ;-)

P is for Prickletac.  

I hear it’s face day, so here’s my face XD. But also, look at the shiny new hat that I test-knit for @thechronicferuchemist ! It probably should be blocked, but even without blocking I’m super happy with how it came out :D (Her post about the hat is here)

PSA for Mistborn Cosplay

I was at a craft store today (this is always a dangerous thing) and was looking for a thing on the baking supplies aisle and I made a connection:

If you ever want vials of things that look like metal that you can actually for real eat, this is where you should go. There is such a thing a powdered food coloring and it comes in metallics. There are also vials of things that are basically silver and gold food grade confetti.   

I'm not certain what kind of liquid I would suspend them in and you would still have to figure out how to pull off your special effects after drinking them, but there is a way to have vials of "metal" that aren't poison.