Archive for Math

Smarterer


As a Bzzagent, I get to try out new products and services for free or at a discount. Most recently I was invited to try out Smarterer, a website that features quizzes on all sorts of things like facebook, wordpress, twitter, bzzagent and even advanced mathematics! Just to let you know this website is free for everyone, so you have no reason not to give it a try.Here are my top scores.

The way it works is you answer questions on the topic of your choice and you are awarded points for getting correct answers and you loose points for getting incorrect answers. You’re timed and the faster you answer correctly the more you improve your score. But that’s not the only way to earn points, you can also add questions to a quiz. You earn more points if other users rate your questions as being worthy and based on how difficult other users find them.

After you’ve taken some tests you can put up to five scores on a badge (like mine above) and post it onto your blog or even a resume. It’s great for resumes if you do well on tests for software in your job field like MS Word, Excel, Power Point, SolidWorks, Auto CAD and even programming languages. You can post individual scores to your twitter of facebook account once you’ve linked them with your smarterer account.

I really recommend trying this website out. I had no idea at how much I didn’t know about software and websites I had been using forever like MS Word and Facebook. Just taking the quizzes and seeing the right answers helped me learn more about what I could do with them. The only down side is that I can’t go back and re-answer those questions to improve my score. I can only answer new ones or add more questions.

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Why You Should Understand Volume and Density In Real Life

I realize that I was born with a math teacher brain, which caused me to notice two things that led me to write this post.

The first thing was a commercial for Hershey’s new aerated chocolate.

My mother’s immediate reaction to the commercial was that it was a ripoff because you would be getting less chocolate. But I said that you cannot be sure of that until you look at the net-weight on the package and compare it to a normal Hershey bar, and see if there is any difference in price. I have no pictures, but during my most recent trip to CVS I noted that a normal Hershey bar’s net weight was 1.55 oz while the aerated chocolate’s net weight was 1.45 oz. For the same price you are getting 0.10 oz less chocolate with air-bubbles in it. Not worth it for me, but if you’re being calorie conscious this could be a help. But if you really wanted to be healthy you wouldn’t be eating a whole bar of chocolate in the first place.

Something interesting to think about is how we can use simple algebra to figure out how much more money Hershey makes on the aerated chocolate. Set up the following ratio:

(aerated/ normal) = 145/155 = x/100

Solve for x and you get 93.5. Which means the aerated chocolate’s weight is about 94% of the normal chocolate’s weight. Hershey would prefer you buy the aerate chocolate because since both bars are the same price, they make about 6% more. Keep in mind I’m not taking into consideration how much it costs to run the machinery that aerates the chocolate, but I’m assuming it can’t be much.

The second thing was the shape of the bottle of nail polish that Christal sent me! It’s the Funky Fingers nail polish pictured here with a few other bottles of nail polish in my house.

from left to right: sally hansen's quick dry, funky fingers, wet n' wild, NYC quick dry

Would you expect that nail polish bottles were set at some standard volume size and that these would all hold the same amount? They’re not. In fact they all have different net weights listed on the bottom. My mom’s Sally Hansen nail polish was the most expensive one there, costing $5. The NYC quick dry and Wet n’ Wild were each $2. And according to the internet Funky Fingers seems to retail around $2-$6 a bottle.. though I think the more expensive ones were just people trying to make a profit on e-bay.

Based only looking at the bottles I would have guessed the order from least to greatest would have been NYC, Wet n’ Wild, Sally Hansen, Funky Fingers. But looks are very deceiving, pictured below are the bottles arranged in order from least to greatest, based on the net weight written on the bottom of the bottle.

So the most expensive one has the least amount of product. A typical student would probably say you should buy the cheapest one that holds the most, but this is where the real life applications come in and taint the purity of math. You should buy the one that best suits your budget, and has a quality that you are satisfied with. If one brand requires more coats than another brand, you’re not exactly saving money by buying that one even if it has more product in it. It’s really a matter of what you want and how much you are willing to spend. But that doesn’t mean that you shouldn’t be mathematically knowledgeable about how much you are getting at the same time!

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Back To School Next week

So I quit my job at the movie theater a while ago. I’m pretty glad I did. It had awesome fringe benefits (free movies, free movie posters, free popcorn), but it came with a downside. That downside being the stupidest customers ever. People who don’t know what they want to see and want *you* to decide for them, people that bitch when you ID them for R movies, immigrants who can’t speak English and make almost NO effort to do so and the shitty parents who have no problem taking their 5 year olds into R-rated movies (specifically The Hangover). Plus this job killed my summer, I didn’t get the chance to prep for any of the exams I wanted to and I never got driving lessons.

Next semester I’ll be student teaching 6th graders. I’m looking forward to it, but I have a feeling I won’t have a life since education classes require papers. I’m also taking two math classes, Euclidean Geometry and Abstract Algebra.  The Geometry professor is the best professor ever according to everyone. Likewise, according to everyone Abstract Algebra is the *worst* class ever no matter who you take it with, but I made sure to take it with the best prof out of the three who teach the class.

I also had the most alcohol I’ve ever had in my life in the past two weeks (and it wasn’t much). A bit more than half a normal serving of mead (at the Renn Faire) and about 3/4 of a beer. Having Crohn’s Disease I was warned against drinking alcohol by the internet, but my doctor told me that you need to live your life and as long as I didn’t go too extreme I should be fine. I had no problems with the mead, it was awesome! However, I am *never* drinking beer again. Even the alcohol free kind. NEVER EVER AGAIN. It made me puke, get the runs, have chills and left me with stomach pains that days latter still showed up on occasion.

So upon doing research I discovered that a good number of people with Chrons or Colitis are ok with wine but not with beer. One study claims that its based on the sugar content of the drink, but I was fine with the sweet mead. I think its because beer is heavily yeasted. When I was looking up how wine and beer were made, the first recipe ever found for beer included throwing in bits of undercooked bread to act as a yeast (since they had no real yeast back then). The first recipes for wine only consisted of letting smashed grapes sit long enough. These days yeast is added in the wine making process, but way less than is added in the beer making process (which is a much more confusing process).

I’m a bit saddened at this, since I did enjoy the taste of the beer I had and was looking forward to trying a legit German beer or going to an Oktoberfest. But then again I’m thankful I could tolerate the mead since many people with Crohn’s can’t tolerate any alcohol period. Mead is the true drink of my ancestors anyway, though I will never be able to truely enjoy a hofbrauhaus 😦 I never even had the desire to get drunk… I just want to have one beer with a German meal and fellow Germans and Germans at heart :D. Who knows it might happen in the future if I can go into remission long enough, or in the future should I decide to get pregnant and my Crohn’s goes away while I am pregnant I can drink sometimes. And don’t bitch about what I just said. One glass of wine will not hurt a baby. Both of my grandmothers smoked, drank and took medication while pregnant with my parents, aunts and uncles and all of them turned out fine, except one of my uncles having been born with kidney problems.

All of that aside I both want to and don’t want to go back to school right now. But I am looking forward to the fall, Halloween, comic-con and Thanksgiving. I also think I’ll enjoy student teaching. The main thing I’m worried about is the fact that the girl I was paired with for the fall semester doesn’t speak English too well, and we have to write joint papers together. I’ve been able to work with people who were still learning English in the past well enough, but speaking English and writing in English and two very different things. I already know I’m going to be the editor all the time. Not something I’m happy with.

I’ll end with a picture of something I’d love to do to an honors class on April Fools day. (Wouldn’t do this to a normal class out of sympathy for the slow kids).

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The Math Behind Why The House Always Wins

As a part of the course I took this past semester on teaching math in secondary schools, I (with a small group of my classmates) taught the class a unit on data analysis and probability. I also had to write a few short papers about certain things we covered in our lesson. What follows will be a merged summary of two of my papers.

Before I begin I’ll provide some vocabulary for those of you that never learned these terms or learned them and have since forgotten them.

Expected Gain: How much money we should expect to gain if we continue to gamble on one game for a long time.

Fair Game: A game in which the expected value is equal to zero. In other words if we played a fair game for a long time we should break even.

Unfair Game: A game in which the expected value is positive (we will profit from the game) or negative (we will lose money by playing the game).

Now, let’s consider a game where you win $4 if you roll a fair six sided die and it lands on “1” but lose $1 if it lands on any other number. Would you be tempted to play this game because winning $4 is more than loosing $1? The way we calculate the expected gain of this game is to multiply the chance of winning (1/6) in one play by the amount we would win ($4) in one play and add that to the the chance of loosing (5/6) in one play multiplied by how much we gain for loosing (-$1). The equation looks like this:

(1/6)($4) + (5/6)(-$1) = -$0.16666….

Our expected gain is equal to about negative 17 cents. Basically it means that if we continue to play this game for a long time, we should expect to lose 17 cents on average. If we won $5 for winning instead of $4 the expected gain would be 0 and this game would be fair.

Now you might be thinking that my example was stupid because no casinos have a lame game like the one I mentioned. If you are, I have two points to make (1) idiots will bet on anything, and (2) they might not have this game but they have others like it. Consider the game of roulette.

There are plenty of casino games I could discuss, but roulette is the simpliest to understand. There are many ways you can bet on the roulette wheel, evens and odds, red and black, a third, a single number, etc. I’ll discuss the expected gain for when we place our bet on evens or odds. The payout is 1:1 (if we bet $1, we win $1 and if we loose we loose the $1 we bet).  Do you think our chance of winning is 50:50?

If you think that half of the wheel is even and half of the wheel is odd you’re wrong because you’ve failed to noticed the two green “0” slots. If you think that more of the numbers are even because in mathematics zero is, in fact, an even number you’re also wrong because it’s not that way in the casinos. Did you notice that our chances of winning are not 50:50, yet our payout is 1:1? Our chances of winning are 17:36. The expected gain in this case is:

(17/36)(1) + (19/36)(-1) = (-323/630) =  -0.05555…

This means that on average we can expect to lose about 5.6% of what we’re betting.

The reason that the house always wins is because *every* game they have is unfair in their favor. The only exception is Blackjack (21), and it’s only an exception if you can count cards. They either rig the odds or payouts of every game so that they have some sort of advantage over you. Even if we win big, it doesn’t hurt the casino because our win is made up for by all of the other player’s losses. So there you have it, the math behind why the house always wins.

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The “math” Behind the Rapture (2011)

You may have noticed that this is listed under my category for “math” posts but this is not a math post. This is a post about a piece of pure bullshit.For those of you that don’t know, here’s how the “math” goes:

By Camping’s understanding, the Bible was dictated by God and every word and number carries a spiritual significance. He noticed that particular numbers appeared in the Bible at the same time particular themes are discussed.

The number 5, Camping concluded, equals “atonement.” Ten is “completeness.” Seventeen means “heaven.” Camping patiently explained how he reached his conclusion for May 21, 2011.

“Christ hung on the cross April 1, 33 A.D.,” he began. “Now go to April 1 of 2011 A.D., and that’s 1,978 years.”

Camping then multiplied 1,978 by 365.2422 days – the number of days in each solar year, not to be confused with a calendar year.

Next, Camping noted that April 1 to May 21 encompasses 51 days. Add 51 to the sum of previous multiplication total, and it equals 722,500.

Camping realized that (5 x 10 x 17) x (5 x 10 x 17) = 722,500.

Or put into words: (Atonement x Completeness x Heaven), squared.

“Five times 10 times 17 is telling you a story,” Camping said. “It’s the story from the time Christ made payment for your sins until you’re completely saved.

“I tell ya, I just about fell off my chair when I realized that,” Camping said.

Putting his interpretation of the Bible aside (believe me I could say a million things about how wrong it is), he did no math. It makes me even more surprised to learn that this man was a civil engineer. If you haven’t studied a lot of math you may be wondering why I claim that this is not math, but in fact, bullshit. What  this man is doing is pulling numbers out of the Bible and assigning meaning to them that they otherwise do not have, he is then performing random mathematical operations on those numbers and claiming the result has meaning because he got the same result two different ways.

His random numbers weren’t even good ones, they’re all deficient. I mean, if I were to construct such bullshit I would have used perfect or abundant numbers. How the hell a deficient number can represent “completeness” is beyond me. The reason the ancient Greek’s first called 6 a perfect number was because they thought the world was created in 6 days and thought it was cool that the the sum of 6’s proper divisors was twice 6. But even that doesn’t make 6 perfect in the non-mathematical sense, it’s just a name given to a mathematical property. There are also amicable, social and taxi cab numbers. Numbers can have all sorts of cool properties, but that doesn’t give them any real meaning. The number 3 and multiples of 3 appear all over various pagan myths. All that means is that the ancients happened to like the number 3 for some reason.

God created math and the universe. Any meaning numbers have was created by us.

Lastly, what confuses me the most, is that, if this guy was really scrutinizing the Bible, how did he miss that what is doing automatically makes him a false prophet? Jesus said only God knows when the world will end.

The world isn’t going to end in 2012 either, the alien overlords that sped up our evolution are going to come back and call us damn fools for forgetting all of the science they taught us. Or we’ll just go back to the beginning of the Mayan calender in the same manner that we get a new calender after every December 31st 😄

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My Last Number Theory Class

I cannot believe that yesterday was my last Number Theory class. It wasn’t technically since I have my last exam before the final this coming Tuesday, but it was the last “class” class. It does not feel like that class is, or should be over. It feels like there’s so much more I’m supposed to learn. My professor was awesome even though my exam grades haven’t been the best.

No matter what I get on my next exam and final for this course, I can say I’ve learned a lot, most importantly that number theory is my favorite kind of math. It’s pure math, for those of you aren’t familiar there are two types of math, pure and applied. Things like calculus and probability are applied math, full of obvious applications to the real world. Pure math is when you stop caring about whether or not it has applications, in many cases it does, but it might not be immediately apparent.

One of the best things about number theory is that we only have to deal with integers. There’s no approximation because it’s all exact. FYI: I can’t stand approximation (or decimals for that matter). I think it bugs me because even though an approximate answer is considered an answer, I still feel that it’s incomplete.

Another awesome thing I love about number theory is the amount of unproved conjectures and areas of research I could go into. I feel like I actually have a fighting chance of doing something in this field if I can find a pure math master’s program with a good amount of number theory in it. There are even a few conjectures mentioned in class that I plan on playing with this summer just for the fun of it. I’ve heard a lot of people talk about how hard and intense number theory is but I don’t really understand why, unless it’s because you need to understand the proofs to understand whats going on.. but I feel that that’s true of all math.

If you’re still reading and have not understood a thing I was talking about, I applaud you! Now I offer you a few of the fun facts my professor told us throughout the semester!

– That paper thing they slip over your coffee or tea at Dunkin or Starbucks is called a zarf

– Wilson didn’t prove “Wilson’s Theorem” or even come up with it. It was first conjectured by Leibniz, when Wilson conjectured it later independently, his teacher stole it and published it. It was finally proved by LaGrange. But Wilson gets the credit.

-Fermat’s Last Theorem wasn’t the only theorem he didn’t write out because he didn’t have enough room on the paper before he went and died. The same is true of Fermat’s Little Theorem. It was finally proved by Euler.

-The numbers (6 x 6 x 6), 666 – (6 x6) and 666 make up the sides of a right triangle. The area of this triangle is 666,666.

-The Law of Quadratic Reciprocity was first proved by Gauss at the age of 18 in 1796. He did six more proofs of it through out his life. As of 2000 there are 192 proofs of it.

-Euler had a thing for coming along and proving unproved conjectures

-Gauss was a genius, and was quoted “Mathematics is the queen of the sciences and number theory is the queen of mathematics.”

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Some Statistics

Time for another math related post because I haven’t done one in a while!

Currently I’ve been really busy working on this huge arse project for my math education class (it counts for a ton of my grade).  I’m in a group with five other people and we have to teach our class a unit on probability, and fill a 5 inch binder with lesson plans and other educational goodness. We already taught our first two lessons and have three to go.

During our first lesson we talked about new ways of visually representing data, aside from xkcd’s awesome maps of the internet (2007) and (2010) we also showed them word clouds. Word clouds are clouds of words, where the most frequently used words are the biggest and less frequently used words are smaller. You can make them at wordle.net . Here are some that I’ve made of my blog and the blogs of two of my friends.

Here are links to their blogs if you’re interested: http://kristinamirasol.net/, http://chubbyriceball.wordpress.com/

Another interesting thing that I recently rediscovered is some of the other things wolfram alpha can do besides act as a super calculator.

If you put in your gender, age and height it will tell you what you should weigh. And what your appropriate lung capacity should be and how much blood should be in you and other interesting tidbits of that source.  (I don’t know where they got 131lbs for a 5’5″ woman though. I had been told that healthy weight was 100 lbs for the first 5 feet and 5 more pounds for each additional inch, give or take 5 pounds, was a healthy weight from my cousin who is a nutritionist. That would make a healthy weight be between 120 and 130 pounds.  I don’t think I’ll ever weigh 130 pounds. I’ll be lucky if I can get back up to 117.)

It will also tell you how many days and weeks you’ve been alive if you put your birthday in it. It’s also a dictionary! And for those of you that didn’t grip the meaning of “super calculator,” it will do integrals for you *and* show you the steps! It will factor huge expressions and expand them among so many other awesome things!

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