2 New Palindromes
1- Was it a car or a cat I saw?
and
2- 1122211
The symmetry behind this one is interesting because while it is a fairly simple palindrome, it is the
solution of a palindrome divided by ANOTHER palindrome. Specifically, 12344321 / 11. These divided are both palindromic numbers, simple ones, and their result after division is another palindrome, so I thought that was kind of interesting. Also while researching I ran across a hypothesis that any palindromic number with an even number of digits is divisible by 11, so think on that as well.
Sources:
http://www.rinkworks.com/words/palindromes.shtml
Tuesday, April 14, 2015
Thursday, March 19, 2015
Pop Goes the Economy
So I got this idea a few years ago, when my old math teacher and I went kayaking in DC. We would talk about anything, from stupid 80's movies, to strange mathematical concepts, and a lot in between. Anyway, the point is, one day we mentioned collecting quarters. She explained that she collected quarters, as did I, and 50 cent coins. This is where it gets interesting: we started thinking about just how many people collected the 50 state quarters. That's gotta be a lot of people, and in turn, a lot of quarters. And all those quarters are out of circulation, but they exist, with the potential to be put back in. So what if, one day, all of them WERE put back in? What would happen? Would anything happen? Let's say, that by some miracle, out of the 300,000,000 people in this country, 100,000,000 seriously collect enough quarters to have the 50 states. That's 50 quarters a person. So, 50 quarters times 25 cents equals $12.50. $12.50 times 100,000,000 is $1,250,000,000. 1.25 billion. Sounds like a lot, but in the scale of the economy, its not too much. But what about even more SERIOUS collectors, the people who have collected the 50 states over... 3 times. That's 150 instead. To make things even MORE complicated, just think about how many REPEATS the first 100,000,000 people had. They must have had 20 or 30 repeats each. Let's say 20. So those original 100,000,000 now have: [20 (repeats) + 50 (states) ] * .25 (dollars per quarter) *100,000,000 (people) = $1,750,000,000.
THEN we have to add on the serious collectors. Lets say they have every state 3 times over, and 20 additional repeats apiece, like the others. [20 (repeats) + 50 (states) ]* 3 (full sets) * .25 (dollars per quarter) *10,000,000 (people)= $52.50* 10,000,000= $525,000,000. Now add that on to the earlier 1.75 billion dollars, and we get 1.75 billion plus 0.525 billion= $2.275 billion or $2,275,000,000. Now if all that got pumped back into the economy, in one night, it might cause something. If in one moment suddenly over 2 billion dollars got put into circulation, it might cause a slight dip in the economy, due to the value of the dollar decreasing due to over abundance of in circulation money.
Who knows though, what if someday, everyone in the USA has 50 state quarters, repeats and all, and dumps THAT back in. It'd be fun to watch thats what.
THEN we have to add on the serious collectors. Lets say they have every state 3 times over, and 20 additional repeats apiece, like the others. [20 (repeats) + 50 (states) ]* 3 (full sets) * .25 (dollars per quarter) *10,000,000 (people)= $52.50* 10,000,000= $525,000,000. Now add that on to the earlier 1.75 billion dollars, and we get 1.75 billion plus 0.525 billion= $2.275 billion or $2,275,000,000. Now if all that got pumped back into the economy, in one night, it might cause something. If in one moment suddenly over 2 billion dollars got put into circulation, it might cause a slight dip in the economy, due to the value of the dollar decreasing due to over abundance of in circulation money.
Who knows though, what if someday, everyone in the USA has 50 state quarters, repeats and all, and dumps THAT back in. It'd be fun to watch thats what.
Tuesday, March 3, 2015
TPC Probability Blog Post
I decided to go on a bit of a tangent (ha) for my blog. We've been discussing probability and dependent/independent events. I want to write about The Monty Hall Problem, also known as the Game Show Problem. The idea is this: You are given the choice of three doors, behind one is a car and behind two are goats. You choose Door 1, the host opens up door 3, to reveal goat. At this point he asks you if you'd like to switch choice of door or stay with his current choice. The big question is, is it in your favor to switch or not?
For a lot of people, the answer is: Doesn't matter. When there are only two doors left, you have a 50/50 chance of getting the car, so switching will do you no good. In fact, some people even claim it's better to now switch, because even with a 50/50, the host is trying to trick you into choosing the wrong door by switching. They're trying to use reverse psychology. The flaw in that thinking goes back to the base of the problem though, in that it's not a 50/50. Its a 2/3 to 1/3 chance if you switch. The idea is that once one door has been opened, you can choose to switch, and now you have the 1/3 chance of your new door, as well as being able to discount the 1/3 from the door opened to reveal a goat. Leaving only 1/3, to be added to potential successes. If this sounds weird, and I know it does, Im including a link to a diagram that may help. Please look at it, it helps a lot, and it looks a lot like the tables we're working with right now.
https://www.google.com/search?q=monty+hall%3B%3B+problem+diagram&safe=off&es_sm=91&biw=1280&bih=664&source=lnms&tbm=isch&sa=X&ei=13L2VJz3DNWmyAT__oCgCw&ved=0CAYQ_AUoAQ&dpr=0.9#imgdii=hKfYzkMgRnZYPM%3A%3BlDjQkxxSg4LaeM%3BhKfYzkMgRnZYPM%3A&imgrc=hKfYzkMgRnZYPM%253A%3BTfLPnLkFrv2UlM%3Bhttp%253A%252F%252Fwww.ashford.zone%252Fimages%252F2008%252F03%252Fthemontyhall.jpg%3Bhttp%253A%252F%252Fwww.ashford.zone%252F2008%252F03%252Fthe-monty-hall%3B500%3B452
For a lot of people, the answer is: Doesn't matter. When there are only two doors left, you have a 50/50 chance of getting the car, so switching will do you no good. In fact, some people even claim it's better to now switch, because even with a 50/50, the host is trying to trick you into choosing the wrong door by switching. They're trying to use reverse psychology. The flaw in that thinking goes back to the base of the problem though, in that it's not a 50/50. Its a 2/3 to 1/3 chance if you switch. The idea is that once one door has been opened, you can choose to switch, and now you have the 1/3 chance of your new door, as well as being able to discount the 1/3 from the door opened to reveal a goat. Leaving only 1/3, to be added to potential successes. If this sounds weird, and I know it does, Im including a link to a diagram that may help. Please look at it, it helps a lot, and it looks a lot like the tables we're working with right now.
https://www.google.com/search?q=monty+hall%3B%3B+problem+diagram&safe=off&es_sm=91&biw=1280&bih=664&source=lnms&tbm=isch&sa=X&ei=13L2VJz3DNWmyAT__oCgCw&ved=0CAYQ_AUoAQ&dpr=0.9#imgdii=hKfYzkMgRnZYPM%3A%3BlDjQkxxSg4LaeM%3BhKfYzkMgRnZYPM%3A&imgrc=hKfYzkMgRnZYPM%253A%3BTfLPnLkFrv2UlM%3Bhttp%253A%252F%252Fwww.ashford.zone%252Fimages%252F2008%252F03%252Fthemontyhall.jpg%3Bhttp%253A%252F%252Fwww.ashford.zone%252F2008%252F03%252Fthe-monty-hall%3B500%3B452
In reality, it is a 2/3 to 1/3 chance of success if you take the door switch. This also shows that the choice of doors are not independent of one other. I include that just to tie it in a bit more to our current lesson.
Thursday, February 19, 2015
Innumeracy in the USA and Why Most Don't Care
First, the rival fast food chain was A&W, and the title is "Why Do American's Stink at Math?"
In the USA, our history has been defined by the idea of self sufficiency and growth. From our origins, we have often been very self reliant and thoughtful. As the nation grew, new thought processes entered the heads of many, one such idea being capitalism. In our country, capitalism is the driving force behind our economy, and in turn is directly responsible for social settings. The rich and the rich will mingle, the middle class will keep to themselves etc. Capitalism relies on a large working class, (the 99%) to maintain large corporations and keep them running so that the economy doesn't falter and we can continue to mass produce goods of every nature for distribution. However, most of this work does not require much math. Every job in America requires reading and writing capabilities, and is considered a standard due to it's constant every-day, every-minute use. However, in the real world, where you're only expected to keep the machine running, and leave the brain work to the 1% that reaps the benefits, most people are left not needing math. People aren't upset about innumeracy because it's not viewed as a necessity by the masses. It's not viewed as a necessity by the masses because the masses don't need to be smart. It's actually WORSE if we're smart, because then the few people who sit at the top have to deal with us. No, to push one button all day over and over, or organize documents for your direct boss, that doesn't take much thought of math. We are conditioned to accept the thought of not needing thought. "if we keep ourselves to ourselves and never question the order, we'll get by." This sheep mentality is what a system like capitalism in our country requires, and universal numeracy could endanger that. People need to be able to read and write as the most basic skill, so that is considered a MUST, and even to do basic jobs, so the nation as a whole enforces the literacy of people. Numeracy is not such a basic skill, and despite the ease with which we could make it such, it could counteract the goals desires of the men and women who sit on top our country and economy: to make more money for themselves. It all goes back to education, its easier to to herd the cattle than the thoughtful humans.
In the USA, our history has been defined by the idea of self sufficiency and growth. From our origins, we have often been very self reliant and thoughtful. As the nation grew, new thought processes entered the heads of many, one such idea being capitalism. In our country, capitalism is the driving force behind our economy, and in turn is directly responsible for social settings. The rich and the rich will mingle, the middle class will keep to themselves etc. Capitalism relies on a large working class, (the 99%) to maintain large corporations and keep them running so that the economy doesn't falter and we can continue to mass produce goods of every nature for distribution. However, most of this work does not require much math. Every job in America requires reading and writing capabilities, and is considered a standard due to it's constant every-day, every-minute use. However, in the real world, where you're only expected to keep the machine running, and leave the brain work to the 1% that reaps the benefits, most people are left not needing math. People aren't upset about innumeracy because it's not viewed as a necessity by the masses. It's not viewed as a necessity by the masses because the masses don't need to be smart. It's actually WORSE if we're smart, because then the few people who sit at the top have to deal with us. No, to push one button all day over and over, or organize documents for your direct boss, that doesn't take much thought of math. We are conditioned to accept the thought of not needing thought. "if we keep ourselves to ourselves and never question the order, we'll get by." This sheep mentality is what a system like capitalism in our country requires, and universal numeracy could endanger that. People need to be able to read and write as the most basic skill, so that is considered a MUST, and even to do basic jobs, so the nation as a whole enforces the literacy of people. Numeracy is not such a basic skill, and despite the ease with which we could make it such, it could counteract the goals desires of the men and women who sit on top our country and economy: to make more money for themselves. It all goes back to education, its easier to to herd the cattle than the thoughtful humans.
Sunday, February 1, 2015
Big: Not the Tom Hanks One
So how big is big really? And how can you wrap your mind around the concept? Let's start with the idea of water and some basic chemistry. One mol of water, is 6.022 x 1023 molecules of the stuff. For a visual idea, not that it'll help much, that's 602,200,000,000,000,000,000,000 molecules of water. That's a lot of water... or is it? Actually that many water molecules is only about 18 grams of water, or a small sip. Weird, all those molecules, and yet still such a small amount of water. So here's the tricky part. Imagine the following: oceans. Yeah, that's a LOT of water molecules.
Let's try the math on this. Every cubic milliliter or centimeter of water is 1.0 grams. There are 133,800,000,000,000 cubic centimeters (and in turn milliliters) of water on earth at any given time. So that's 1 gram per cubic centimeter, so 133,800,000,000,000 grams of water. For reading, that's one hundred and thirty three trillion, eight hundred billion grams of water. So, if there are 6.022x 1023 molecules of water in ~18 grams, we can do the math. 133,800,000,000,000/18 = 7,433,333,331,111 So now multiply THAT number by the number of molecules of water in a mol, and you get (6.022x 1023) x (7,433,333,331,111) = 4.4763533 x 1036 molecules of water on earth at any given time. Translated, 4,476,353,300,000,000,000,000,000,000,000,000,000
OR Four -Undecillion, four hundred and seventy six decillion, three hundred and fifty three nonillion, three octillion. That's a lot of water molecules.
Let's try the math on this. Every cubic milliliter or centimeter of water is 1.0 grams. There are 133,800,000,000,000 cubic centimeters (and in turn milliliters) of water on earth at any given time. So that's 1 gram per cubic centimeter, so 133,800,000,000,000 grams of water. For reading, that's one hundred and thirty three trillion, eight hundred billion grams of water. So, if there are 6.022x 1023 molecules of water in ~18 grams, we can do the math. 133,800,000,000,000/18 = 7,433,333,331,111 So now multiply THAT number by the number of molecules of water in a mol, and you get (6.022x 1023) x (7,433,333,331,111) = 4.4763533 x 1036 molecules of water on earth at any given time. Translated, 4,476,353,300,000,000,000,000,000,000,000,000,000
OR Four -Undecillion, four hundred and seventy six decillion, three hundred and fifty three nonillion, three octillion. That's a lot of water molecules.
Friday, January 16, 2015
Transcendentalism
Transcendentalism
The word Transcendental means "of or relating to a spiritual or nonphysical realm. Men such as Thoreau or Emerson focused their writings and theories on the world that was non physical, a world outside our ability to touch and directly interact with. In math, Transcendental Functions are functions that transcend algebra, that in one direction or multiple directions, go on to infinite. These functions cannot be limited to a finite sequence or list, and as such "transcend" our ability to really comprehend them. The reason for our studying these functions is because in calculus, we deal a lot more closely with such ideas as infinite, and we do so constantly.
Yeah, every 2 weeks sounds good for due dates.
The word Transcendental means "of or relating to a spiritual or nonphysical realm. Men such as Thoreau or Emerson focused their writings and theories on the world that was non physical, a world outside our ability to touch and directly interact with. In math, Transcendental Functions are functions that transcend algebra, that in one direction or multiple directions, go on to infinite. These functions cannot be limited to a finite sequence or list, and as such "transcend" our ability to really comprehend them. The reason for our studying these functions is because in calculus, we deal a lot more closely with such ideas as infinite, and we do so constantly.
Yeah, every 2 weeks sounds good for due dates.
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