Reminder!!

Just a reminder, on Friday, we are going back to the original schedule with Annis posting on Mondays and Tuesdays, me on Wednesdays, Saturdays, and Sundays, and Kazuma posting on Thursday and answering the problem on Friday. I guess it will be a weekly question rather than a daily problem. 

Problem of the Day #8

I'm covering for Kazuma because we usually work together on posts but I was late for the meeting. It is completely my fault.

Figure out the next part of this pyramid:

1
11
21
1211
111221
312211
13112221

So, what comes next? This will help you sharpen your pattern senses.

All those Greek Alphabets, well at least half...

I realized after some research, all of the Greek alphabet letters have some correlation to math. I actually studied the Greek alphabet, as did Kazuma and Strix. Anyway for the first letter, alpha. Alpha has multiple appearances in mathematics. A few of them include the first angle in a triangle and the reciprocal of the sacrifice ratio. The sacrifice ratio is dollar cost of production loss/ percentage change in inflation. Go here to find out just a tiny bit more about the sacrifice ratio! For beta, the beta function! The beta function is also called the Euler integral of the first kind.
The beta function: 
It's kind of confusing so go here. It's quite funny, the next letter is gamma. Gamma is for the gamma function, or the Euler integral of the second kind which is, also on the above link. Delta is for change! There is really no function or term for delta but it mostly is used to describe changes in plot points or coordinates. Epsilon denoted as small positive infintesimal quantities. Yay! More functions!! Zeta is for the Riemann-Zeta function. The zeta function is this:

$$$$ζsn1∞1ns

Confusing, right? It's used to analyze the prime number theorem and Dirichlet's theorem.

Eta for the dedekind eta function. It's the upper half plane defined as  . Theta is just used to represent an unknown angle in geometry. Iota is the square root of -1, also called the imaginary unit. Kappa is for the kappa curve! Also called Gutschoven's curve, this curve is a two dimensiol algebraic curve resembling kappa. For lambda, so far I've heard of lambda calculus, and the lambda function. I'll just explain lambda calculus. Lambda calculus is a foundational theory consisting of logical symbols and algorithms operating these symbols. Mu stands for the mean of probability distribution. That's it for now, but tune in for the other half of the Greek alphabet! See Ya!

Tessellations

Kazuma is helping me again. :) Tessellations are a pattern of shapes that fit perfectly together. Tessellations are classified as regular, semi-regular, and other tessellations. 

Regular tessellations are repetitions of 1 polygon. There are only three types of regular tessellations. Triangles, squares and hexagons. 

Semiregular tessellations are made of two or more regular polygons. There are 8 semi-regular polygons. For pictures click on this link. 

Other tessellations include demi-regular tessellations but mathematicians disagree on what defines them. 

Some authors define demi-regular polygons as orderly compositions of three regular and eight semi-regular tessellations. Other authors define demi-regular tessellations as a tessellation having more than 1 transitivity class of vertices.
Then, there are tessellations that have curved edges and circles.
Escher is a tessellation artist. He created pieces of art made with objects that can tessellate like the flying horses above. You can make your own tessellation with polygons at this tessellation maker.

 &

Problem of the Day #7

How can you add eight 8s to get the number 1,000? (only use addition)

 &