Some Infinities are Bigger than Other Infinities

Hello, good day to you all!
I'm really sorry about not posting at all, I'm on vacation.
And now we're out of school, we can post more freely and you know, talk about our interests and discuss random things rather than focus on math.
So hello. It's Strix Spell here. I think Kazuma decided that she does not want to post anymore and Annis might, occasionally. I like to keep a schedule but well, that's near impossible now.
As well as talking about math, we can expand it to some more science as well.
Today, I'm focusing on the popular quote by John Green in his new book The Fault in Our Stars which I read and I'm going to review in my other blog.
Anyway, the quote is: "Some infinities are bigger than other infinities."
The thing about infinity, it is endless. It goes on and never stops, like a set of numbers (1,2,3,4...) So how are some infinities bigger than other infinities?
Hazel incorrectly explains it as: the set of numbers between 0 to 1 is a smaller infinity than the set of numbers between 0 and 2. While that is untrue, the statement some infinities are bigger than other infinities is still true.

That video explains a lot better than I can. But, if you are too lazy to watch the video, here is a random summary. While the set of numbers between 0 and 1 is the same number as the set of numbers between 0 and 2, we know that the set of numbers between 0 and 1 is bigger than the set of positive integers (1,2,3,4...). 

Okay, I can't explain so haha! You have to watch the video to understand. 

Anyway, basically, what I am trying to point out is that some infinities are bigger than other infinities. Yay!

Goodbye Answers

The answer key, also known as Tricky and Twisted Math has been reverted to draft because Kazuma, Annis, and I are doing a class thing and we need the students to figure it out on their own rather than cheat so, sorry!

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.

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.

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Problem of the Day #7

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

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Problem of the Day #6

Angela has 71 cents. What is the least number of coins she can have?

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Problem of the Day #5

Ok, I forgot to cover for Kazuma so I'm doing three problems today. Kazuma will be helping me.

The problem:

If one nickel is worth 5 cents, how much is half of one half of a nickel worth?

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e

e is a mathematical constant. A mathematical constant is any well-defined real number that is significantly interesting in some way. e has a value of about 2.718. e is an irrational number. It is named after Leonhard Euler and can also be called Euler's number because Euler proved e is an irrational number.
You can calculate e with this formula: 1 + 1/1! +1/2! +1/3! +1/4! +1/5! + 1/6! + 1/7! and so on so forth. if calculated out, the first few terms are 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 = 2.718055556. 
e is found in many interesting areas. To memorize e, remember this sentence:
to express e remember to memorize a sentence to simplify this.
(count the letters).
The value of e is used to find a nonlinear increase or decrease. e occurs naturally with some frequency so it is the base of natural logarithms.

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next time: logarithms

Problem of the Day #4

Chiyo is picking between 7 different candy canes to put on her Christmas tree. However, she only wants 3 to go on the tree. What is the number of combinations of candy canes Chiyo can pick if she is only picking 3 candy canes at a time?

Problem of the Day #3

The cylinder's diameter was 4 inches and it was 8 inches tall. Shiro and Jamie were trying to find the volume of the cylinder Shiro says that you need to do 3.14 times 2 squared times 8. Jamie says that you need to do 3.14 times 4 squared times 8. Who's right? Explain.

Comment your answers!

Problems of the Day #2

Jake bought two rectangular containers of coffee powder. The decaf coffee container is 1/4 feet long, 2 inches wide, and 7 inches tall. The regular coffee container is 3 inches long, 1/4 feet wide, and 3/4 feet tall. Which coffee container would hold more coffee powder?

Comment your answers!

Pythagorean Theorem

Pythagoras, a Greek mathematician, created the Pythagorean Theorem. It's used for finding the lengths of the legs or hypotenuse of a right triangle.

Pythagoras, a Greek mathematician, created the Pythagorean Theorem (). It's used for finding the lengths of the legs or hypotenuse of a right triangle. He discovered that the total area of the two smaller sides were equal to the largest side (c or the hypotenuse).

Link(s):


Pythagorean Theorem

Quick Scheduling Change!

If you haven't noticed, we are trying to post every day. Since we don't have much information on, we will try to have at least three posts every day (one from Annis, Kazuma, and Strix). We apologize for the confusion.

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Problem of the Day #1

Kitti bought 3 water bottles, 2 crayon boxes, and 4 strawberry Japanese sodas. The water bottles are half the cost of the soda each and the crayon boxes are 3/4 the cost of the bottles each. About how much did Kitti spend if the sodas are $1.50 each?
Comment your answers!

Proper Real Post #1

Ok, sorry for earlier, we had just created the site and we were feeling deliriously happy. So, anyway, I'm Strix Spell, I'm an administrator for this site. I will keep you posted on what goes on in the math world, complete with opinion on everything. I will be posting on Wednesdays, Saturdays and Sundays because Annis won't let me post every day.
Kazuma will be posting on Thursdays and Fridays. "He" will post some facts on math as well as a riddle on math at the end of each week.
Annis is posting on the new developments (without opinion) and the history of math on Mondays and Tuesdays.
Any questions? Ask away!

UPDATE: ok, I figured it out with the other admins and I'm posting about math, the two sides of the terms, why they are good and why they are bad.

Annis is really weird

Hi! Annis here. I will be covering Math on the Timeline...
For the schedule, Strix will be writing All About MAth  on Wednesdays, Saturdays, and and Sundays. SOrry this blog is not edited very well... or at all. Kazuma will do Math Facts or I dunno whatever "he" wants on Thursdays and Fridays. My blogging takes place on Mondays and Tuesdays.  One last things, it's not my fault if this blog gets screwed up. See ya!

Pi

Hi, I'm Kazuma. I'm in charge of the math facts.

Annis or Strix will cover for me if I forget. 

p.s... pi is 3.1415926535897 and so on...