Tuesday, November 29, 2016

Just For The Record

Today, I

which took, as expected, 100 days. This means I started 100 days ago, which was, by the way, the second day of school.

Also, today I received The Sibley Guide to Bird Life and Behaviour, and was told by it, in no uncertain terms, that birds are reptiles. Ah, well. I was bound to come around sometimes.

Friday, November 25, 2016

I Swear I Did This One Already

I distinctly remember posting this thing about dreams. Huh. Well, to paraphrase myself from that alternate timeline, I've made five different dream journals to date:

jetpack level, finished on December 25th, 2014
Escaping a castle, finished July 5th, 2015
I had a cool dream so, finished February 20th, 2016
On a boat, finished April 18th, 2016
In a fantasy world, finished at 7:00 today, November 25th, 2016

Yay, a list! It's been a while since I've done a list. I need to write other things now, though. Bye!

Wait, one more thing. Jetpack level was 43 pages, Escaping a castle was 35 pages, I had a cool dream so was 42, On a boat 19, and In a fantasy world 32. I just wanted to say that because the old, now-nonexistent post had that information. Bye for real now!

Just For The Record

I finished the series Firefly, and watched the movie, on Monday.
I started watching One Punch Man with my dad on Tuesday.
I went to the tent rocks yesterday (and got some cool pamphlets).
Today, I started and finished Thinger Strangs with my family.
Today, I manned up and did the algebra of the general formula for Lucas Sequences (as I now know they are called). The old formula, in case you couldn't read it, was
which looks kinda ugly and needlessly complicated. So, with just a bit of algebra, it becomes
which is much better.

Saturday, November 19, 2016

Brady numbers. Brady numbers. The title is acting strange. Help me, friend.

I found the general formula for the Brady numbers. It's Bn = 1571.964902Φ^n + 381.0350976(-Φ)^-n.

I know, potoo friend. I was surprised, too.
Here's the series on the Brady numbers:
https://www.youtube.com/watch?v=D8ntDpBm6Ok
https://www.youtube.com/watch?v=dTWKKvlZB08
https://www.youtube.com/watch?v=PeUbRXnbmms
One thing I like about the general formula is that it's clear to see why every series which increases fibonaccily is connected to the golden ratio, because when a term is divided by the previous term it is:
[(a constant)Φ^n + (a constant)(-Φ)^-n] / [(the first constant)Φ^(n-1) + (the second constant)(-Φ)^-(n-1)]
And, because (-Φ)^-n gets closer and closer to zero as n gets bigger, it can be simplified to:
[(a constant)Φ^n] / [(that same constant)Φ^(n-1)]
And then, because [(a constant)Φ^(n-1)] / [(that constant)Φ^(n-1) = 1, this becomes
Φ^(n-(n-1)) = Φ^1 = Φ
YAY!

Two announcements

I did two amazing things yesterday. First, I found a general formula for every fibonacci-like series in which each term is the sum of the two previous terms, given the two initial terms.
The Fibonacci sequence occurs when A0 = 0 and A1 = 1. The Lucas numbers occur when A0 = 2 and A1 = 1. I'm sure someone else has found this formula, but I haven't seen it on the internet. It was a pretty easy generalization to make, after seeing the Fibonacci series done in Elliptic Tales, and then doing the Lucas numbers as a trial run. Learn more about these series here.

Second I did this word search.
I am very proud.