Rithmatics: Part 2, The Potential For 5 Point Defenses

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.

image

More Posts from Kalynaanne and Others

10 years ago

Hey guys. Iredomi posts their cosmere fanstuff over on sebrukiscrossbow and this includes a collection of lovely cosmere inspired poetry. This is me reading one of their poems. You can find the text of the poem in their original post here.


Tags
1 month ago

oh god I'm back

I know, I know. I said I’d just step out for a second. Maybe touch some grass. Maybe not scroll for hours through a website that is basically a dopamine slot machine designed specifically for me. But here I am. Again.

So, hi. I’ve been avoiding Tumblr like it’s a cursed artifact because every time I log in, I lose entire days to posts about sad wizards, incredibly niche fandom memes, and, let’s be honest, pictures of adorable cute animals. But I return to you now, at the turning of the tide, because someone at a recent book signing mentioned that I really needed to talk to y'all in some other way than an 'automatic repost from my own site.'

Fair. It was never you. It was always me.

Now, that said, I'm still talking about FULL NEGATIVE, the scifi book that I'm crowding over on Backerkit, because, well, it's still live, and will be until April 11. I am actively trying to convince you all to throw money at it in exchange for an absolutely unhinged space opera full of telepaths, betrayals, sexy spies, and—because I’m me—an aggressively overcomplicated plot full of feelings. If we hit our stretch goals, we get more cool stuff. YOU get a very cool book. (And there is a limited edition, numbered version of the hardcover available that will ONLY be available through this crowdfunding campaign. Once that window is gone, it's gone FOREVER.)

If you like X-Men, Star Wars, Jason Bourne, or just generally enjoy watching characters make terrible decisions in space, this book is for you. And if you don’t like those things… honestly, what are you doing here? Go, live a better life. Read something wholesome. Avoid the pain I am about to unleash.

So yeah. Click the link, check out the Backerkit, and help me make this book a reality. And if you see me reblogging cat pictures at 2 a.m.? No, you didn’t. I’m totally working.


Tags
10 years ago
Merry Christmas! And I Hope That Any Of You Who Don't Celebrate Christmas Have A Wonderful Day As Well

Merry Christmas! And I hope that any of you who don't celebrate Christmas have a wonderful day as well :-)


Tags
10 years ago

Dear Cfsbf, 

It has come to my attention that the current logo used on the Coppermind (our wiki for all things Sanderson) was intended as a stopgap measure when it was added five years ago. We are planning to finally fix this and to do a redesign of the main page of the wiki. If you would be interested in helping/being part of this conversation (you don’t have to know about wikis), please reply to this post or shoot us an ask over at harmonys-coppermind :-) Any interest?


Tags
10 years ago

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.”


Tags
1 month ago

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…


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
10 months ago
Spacefunk!
Kickstarter
Space is the place! A collection of science fiction stories and poems by authors of African/African Diaspora Descent.

Hey tumblr, I stumbled across this kickstarter for a sci-fi anthology featuring stories and poems by authors of African and African Diaspora Descent. It sounds cool and when I tried to dig up a tumblr post to reblog about it I couldn't find one, so I'm making it myself.

The kickstarter is running through noon eastern on July 19th, 2024. The pledge level for the ebook with over 40 stories and poems is just $10. For $30 there's an ebook bundle with this new anthology and their previous anthologies (Steamfunk!, Dieselfunk!, Cyberfunk! ,and Spyfunk!). There are also options to get a physical copy of the anthology, cool posters, and more.

If you are interested in sci-fi from voices that are currently underrepresented in the community, go check it out!


Tags
10 years ago

I just finished Brandon Sanderson's The Rithmatist. Now, any time I read a fantasy novel with an interesting magic system, I imagine what it would be like to have said magic (don't we all?).  This magic system seems particularly well suited to me - it calls out to both my math and artistic sides.  I think I could make a rather good rithmatist.  The freaking 9 point circle is an important part of the magic system.  I can't even.  

I bet that the 6 point defenses don't actually require that the 6 points be equally spaced.  I bet they could actually be anywhere as long as you build the rest of the defense properly.  The Mystic Hexagon theorem has got to be relevant to this magic system.  I bet you can even use the Mystic Hexagon theorem to build 8 point defenses where the extra two points come from the line dictated by the Mystic Hexagon.  And when that line doesn't intersect the circle, it would be a natural (possibly required) place to put a Line of Forbiddance. There will probably be rithmatic drawings showing up here...

Also, my math notes often have non-math doodles in them.  <3 chalklings

Melody and Joel are fantastic. I like them a lot. There are things I need to process before you get more about them though.


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
  • 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
  • ed-harrison
    ed-harrison liked this · 9 years ago
  • taisharnumenore
    taisharnumenore reblogged this · 10 years ago
  • taisharnumenore
    taisharnumenore 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