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!

Back to Napier!

By the way, Annis and I are collaborating! :D
You probably figured out this post is about John Napier, but he's a good mathematician. Today, you'll learn about his invention of logarithms!! A logarithm is a quantity representing the power in which a base must be raised to in order to produce another number. The formula is log b( x). Well, it doesn't look like that because the b is below log and x. Anyways, the b is base and the x is the number to be produced. For example, log 3 (9) is 2 because 3 to the power of 2 or 3 squared is 9! Get it??

Well, there is also what is called common logs. Common logs are regular logarithms just by 10s. So, the equation for common logs is log x. So, log 100 is 2 because 10 squared is 100.  Now, you might just be thinking, why the heck do I need logarithms because they seem ridiculous.When they were invented, they were used to calculate big and long numbers because they didn't have calculators, which is really funny because Napier helped invent the calculator. Now, they are used to calculate pH scales, the Richter scale, and astronomers use logarithms too. Engineers use logarithms.
Logarithms are everywhere!
You might be thinking at this point, logarithms seem to be similar to exponents. Well, not exactly. Exponents of a number says how many times that number is multiplying itself. Logarithms are the opposite. It asks the question, what exponent produced this number?

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P.S: I how you enjoy our recent collaborations,because we might just have more!!

More Euler, Less History!

Ok, well first of all, Euler is awesome.However I couldn't really find history on his really cool formula, so I figured I'd just blog normally. Anyways, I thought I'd blog about Euler's formula. Euler's formula, first of all is V-E+F=2  or V+F-E=2. V for vertices, E for edges and F for faces. Basically, this means the number of vertices and faces of a convex polyhedron(Click here for a definition!) will always be 2 more than the number of edges of the same polyhedron. Try it out! If a convex polyhedron(in this case a cube) has 8 vertices, 6 faces and 12 edges, what does the formula look like? That would be 8+6-12=2. You may find that some numbers don't work, but that's probably because your solid is just not a convex polyhedron. However, V+F-E can also equal 1and/or other values, so Euler's characteristic was made. He's pretty smart, huh? Anyway, the general formula is V+F-E=x.That is where Euler's characteristic comes in. Umm... so this is an ultra short blog, read up and  things I already explained here! Because Math is Fun! ;D See Ya!

Look it's Euler!!

The Invention of the Calculator

  I am so sorry for not posting yesterday, but I am posting now. Anyway, you might be thinking, Why are you doing this again??? You already did the abacus, so they are similar. And yes, that's correct, but it's kind of cool, because it relates to another mathematician I blogged about. Blaise Pascal. Pascal first created a sort of calculator. Pascal created it as a way to help his dad handle taxes, not knowing what might become of his invention. Later, Gottfried Leibiniz picked it up, and added the addition, subtraction, multiplication, and divide button on the calculator for easy use. John Napier also added a set of metal rods he called, Napier's Bones, for the multiplication table.  That's basically it. I'll post later today, so do not worry. So, for now, See Ya!

The History of Probability

          Probability: the measure of the likelihood that an event will occur.
There are two types of events in probability: simple events and compound events. Simple events... are simple. Simple events are the likelihood of only one event. A simple event  would be like: What is the probability of rolling a 4 on a standardized die? That would be 1/6. If you don't get that, to calculate simple events, create a ratio of the number of times your number shows up (4 only appears once on the die)to the number of possible outcomes(in this case 6, there are 6 faces on a die). Anyway, to the history. Probability was invented by two French mathematicians, Blaise Pascal and Pierre de Fermat. Pascal should technically be credited more because he really came up with the idea. See, Pascal was prompted with the idea of probability by a popular dice game where you would throw a pair of dice 24 times. You needed to bet on whether or not the dice would both land on 6 at least once.  Pascal then began to correspond(exchange letters) with Fermat. This eventually formulated the basis for theoretical probability. Later, more mathematicians wrote books and developed different styles of probability, so really, Pascal and Fermat's creation was a simple event. #badpun... Anyways, compound events are events with at least two events, like calculating the probability of a 5 on a die and red on a spinner. There are 3 types of compound events: mutually exclusive events, independent events, and dependent events. Mutually exclusive events are two events that cannot both occur. The formula for that is P(A or B)= P(A)+P(B). For example if I wanted to find the probability of landing on blue or red  on a blue, red, yellow, and green spinner, I would solve it like this. P of blue=1/4. P of red= 1/4. 1/4 +1/4=1/2. Therefore, the probability of landing on a blue or red is 1/2. A type of mutually exclusive event is a complementary event. Complementary events are mutually exclusive events that probabilities together are always equal to 1. 1 in the probability world means that it is certain to happen. Independent events are two events that do not affect each other. The formula for that is P(A and B)= P(A) x P(B). Basically, when calculating the probability of a die and spinner, you are calculating independent events. Like the probability of 2 and green. Dependent events are two events that has one event depending on the other. The formula for that is P(A and B)= P(A) x P(B)given A. For example, what is the probability of picking two pink marbles in a row if there are 7 pink and 3 orange marbles in a bowl. Remember, the odds of getting a pink change when you have already picked one out. Answer the marble probability question in the comments below. See Ya!

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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Why are Pages Disappearing?

So, you may have noticed that earlier, two pages: Amazing Math Facts and Math on the Timeline disappeared. Ok, well, we have decided that we are all going to post on the main blog as it is kind of hard to draft posts and have older/newer buttons on a page. I'm sure you all hate scrolling down.
So, sorry for any confusion.
By the way, Kazuma is writing the answers to the questions, not Annis. That was a mixup as well.
So, have fun!
Remember, we post every day so do not forget to check out what's going on every day! If you are too lazy to check the website every day, follow us with your email! Simply enter your email and you will get an email whenever one of us posts which is, every day.
Sorry for being redundant. We need pageviews at least, Annis and I live on pageviews.

The Amazing Abacus

For my first real post, I thought I'd talk about something very important in math, the abacus! It's somewhere pretty near the start of mathematics timeline.
      So what is a abacus, you say?
Well, you probably know what an abacus is. It's used worldwide. But basically, an abacus is a counting frame or board. It's really like an ancient calculator. The abacus looks different depending where it came from. The ones normally used by Americans are colorful and big.

An American Abacus

A Chinese abacus looks quite different.

A Japanese abacus is the same only it has one less bead in the top and bottom section.

The abacus was first found in Sumer more than 4,000 years ago. It moved onto China, Japan, and Africa. Finally, it went into the Western world. The American one goes by tens from top to bottom, but the Chinese one uses 4 on the bottom and then a 5 on the top, meaning it could go up to 9. The 2 extra beads were for those who went by 6s. But mainly, the Chinese ignored the extra beads.

An abacus can actually calculate addition, subtraction, multiplication, division, square roots, and cube roots. Crazy, huh? All that came from a little board of counting beads. That is why it is safe to say that addition is the most important mathematical operation, however it is really the basis of all the other operations. Although, you might think the abacus is so ancient, the abacus is actually still used worldwide as I mentioned before, mostly by merchants in Africa and Asia. My opinion on the amazing abacus? Well, it's amazing alright but you would probably not find me using one, mostly because I don't how. It's actually quite complicated, using an abacus, but I know how to set up numbers. I just can't add, or subtract, or anything like that.  Use this Abacus Tutorial if you want to learn about basic abacus functions. I will post a site on the Links page if you just want to play with a Chinese abacus. For now, See Ya!

The Two Sides of Pi

First of all, what is pi?
Pi is an irrational number, or, a number that goes on perpetually without ever repeating itself. Ever.
For more detailed information, click on this link.
From Annis- Pi is AWESOME! it's this crazy Greek letter symbolizing the ration of the circumference of a circle to its diameter.
Strix - Oi, Annis, stop editing my posts! Seriously! Sorry for that.
Anyway, right, pi is the sixteenth Greek letter. Pi is also used as the ratio (not ration) of the circumference of a circle to its diameter.
Pi can be very useful and very useless.
Pi can be useful because it is used everywhere in math, science, and physics. It's famous for that. Pi is ancient, all the way back to the Mesopotamians. Pi is used to calculate the area and circumference of a circle and used to find the surface area and volume of spheres and cylinders.
But so what? Sure pi is famous, the pop star of the other numbers. But we can do without pop stars like Justin Beiber or Miley Cyrus in the real world. We can surely do without pi. What about those who are not scientists, mathematicians, or physicists? What of the teachers and politicians and artists? They never use pi. There is never a situation where there is a dire need of pi. We use other numbers but not pi and the other irrational numbers. What use is there of a number that never ends? Pi doesn't affect most people.
So is pi useful or useless? Ask yourself and comment the answer.
UPDATE (AGAIN) - It doesn't really matter if pi is useless or not. It is the discovery of something that makes it worthwhile. Ancient civilizations knew that pi was about 3 but they did not calculate like we do. In 1761, pi was proved irrational and since then, we have been trying to calculate it.
Pi was a very important discovery. While we do not use it in our daily lives, it appears in many of our everyday items. Pi defined which civilizations were primitive and which were more advanced.

UPDATE: Tomorrow's post: Math is Golden.

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!