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