WARNING: MATHEMATICAL CONTENT!
As I approach my 'toughest' final of the week (a bridge tournament), I thought I'd share some numbers with you.
A bridge hand consists of 13 cards from a standard 52 card deck. There are 635,013,559,600 hands you can be dealt while playing bridge. You would have to play 24,836,748 hands per day to play every bridge hand over the course of 70 years - that's 287 hands per second.
There are 53,644,737,765,488,792,839,237,440,000 possible hands to be played by the whole table. That amounts to 82,472,935,650,000,000,000 hands a second, played since the earth was created around 4.54 billion years ago.
You have a 566,976 times better chance of being struck by lightning than getting a hand with all of one suit. Surprisingly, you are just slightly more likely to be struck by lightning twice than to get this hand.
You have a .2% chance of having all of the aces, a .00017% chance you'll have all the kings to go along with it, and a .00000000006% chance the queens will join the party. If it is any consolation, you have a 98.7% chance of having at least one of those cards.
Wednesday, December 16, 2009
Monday, December 14, 2009
Figure this one out:
A large sign in the library says:
Looking for a computer?
Go to: http://labs.uwec.edu/OpenSeats/index.asp
You don't have to be a math major to scratch your head at that one...
Looking for a computer?
Go to: http://labs.uwec.edu/OpenSeats/index.asp
You don't have to be a math major to scratch your head at that one...
Sunday, December 6, 2009
A Long Overdue Post
I'll tell ya, not much happens around here. I had two hours to kill before a meeting, so I decided I'd write a blog post, but I got side tracked trying to figure out the location of a point inside a square which maximizes the length of the four lines connecting that point to the squares corners. I didn't really need the fancy computer software I was using: of course it occurs in the four corners. Though a 3-d graph of the values would be kind of nifty. I digress.
I got my first fungal infection, and I suppose that's news to write home about! Everybody tells you that if you don't wear shoes in the showers you'll get all sorts of funk on ya feet, but I acquired my massive fungal infestation on my thigh! It has now spread in little splotches all over my body, after my home remedy fungal ointment proved ineffective, and I spent another five precious days treating a non-existent bacterial infection, per doctors orders. But now my guns are effectively loaded, and the enemy stands no chance.
Final are coming up. Finals week is referred to as "the dead hours", or "dead week" and, in fact, there was even a lengthy article about attempted suicide in the school newspaper. I am happy to report that the prospect of finals week has not brought me to suicide. In fact, it seems to me that a week in which you only have to go to class 2 hours a day is a most desirable week. Granted, 30% of your grade rides on that class, but you have plenty of time to study, and that is an understatement. I have already eyed up a good selection of books in the library (mostly children's books, a genre that I have been delving in to more and more as the "academic" books I am required to read leave me sorely disappointed in "sophisticated" thinking).
And other than that, I am quite out of things to write about, though I should mention that I'm quite glad we are in Year C now, and Luke (my second favorite Gospel, next to John) is the Gospel for the next 50 Sundays!
I got my first fungal infection, and I suppose that's news to write home about! Everybody tells you that if you don't wear shoes in the showers you'll get all sorts of funk on ya feet, but I acquired my massive fungal infestation on my thigh! It has now spread in little splotches all over my body, after my home remedy fungal ointment proved ineffective, and I spent another five precious days treating a non-existent bacterial infection, per doctors orders. But now my guns are effectively loaded, and the enemy stands no chance.
Final are coming up. Finals week is referred to as "the dead hours", or "dead week" and, in fact, there was even a lengthy article about attempted suicide in the school newspaper. I am happy to report that the prospect of finals week has not brought me to suicide. In fact, it seems to me that a week in which you only have to go to class 2 hours a day is a most desirable week. Granted, 30% of your grade rides on that class, but you have plenty of time to study, and that is an understatement. I have already eyed up a good selection of books in the library (mostly children's books, a genre that I have been delving in to more and more as the "academic" books I am required to read leave me sorely disappointed in "sophisticated" thinking).
And other than that, I am quite out of things to write about, though I should mention that I'm quite glad we are in Year C now, and Luke (my second favorite Gospel, next to John) is the Gospel for the next 50 Sundays!
UPDATE: HERE'S TODAY'S WAY COOL MATH PICTURE!
The square measured here has a side length of 10. the two lower axes measure the distance of the point from one of the vertical sides one of the horizontal sides. The vertical axis shows the measure of the segments connecting the point to the corners of the square. Maximum occurs at (10,10, 53.77), though (10,0,38.10) gives a surprising run for it's money! Oh! Maybe this is the next one: find the point at which z/(a+b) is greatest. But of course! (0,0,EXPLOSION!) I'll stop the math humor while I'm not too far behind.
Thursday, November 12, 2009
What Gives!
Now, you don't need to be a math major to conjecture that as we enter the winter, and it gets quite a bit colder, skirts should get longer, and as we move back into the spring and summer months, well then, at least there is a half-ways reasonable excuse for wearing short skirts (though modest is, at all points of the year, hottest, and I'm not refering to temperature). Yet, I am finding that skirts are actually shorter now than 2 months ago! The style goes something like this: wear black leggings that cover your whole leg, and then put the shortest possible skirt on which will, in theory, cover your behind, though it's all really quite optional in reality. This can be represented visually below:
An example of reasonable winter attire:
An example of unreasonable winter attire:
Would it be too cynical to point out that my classes are far easier to understand than my peers?
Wednesday, November 4, 2009
The Hailstone Sequence
So, here is the pretty picture I made today. An explentation is below, if so desired (but count yourself warned).
WARNING!!! MATHEMATICAL CONTENT!!!
The Hailstone sequence is the sequence defined as
If a(n-1) is odd, a(n)=3*a(n-1)+1, and
if a(n-1) is positive, a(n) = a(n-1)/2
Unfortunately I don't have subscripts at my disposal, so the function/sequence bleedover will have to suffice.
While it has yet to be proved, it is thought that the hailstone sequence converges to 1 for any starting number a(n). I was interested in the number of steps it took to reach one. For instance, starting number 2 obviously takes 1 step, and 4 takes 2. 3 takes 8 steps, while a starting number of 5 only takes 6. The graph then displays on the X-axis the starting number, and on the Y-axis the number of steps (for lack of a better word... perhaps "iterations"?) it takes to arive at one. I'll admit I stole the idea for such a graph from Wikipedia, but they only went up to 9,999, so I consider myself the victor, even more so if Excel could have more than 16384 columns, which my buddy pointed out is 2^14! He's a computer science major, so a more sophisticated graph may be forth coming.
On another note, a Saturday morning impromptu math class (a full 6 days of quality education for a 5 day price!) to learn about mathematical induction was scheduled. I am most excited!
WARNING!!! MATHEMATICAL CONTENT!!!
The Hailstone sequence is the sequence defined as
If a(n-1) is odd, a(n)=3*a(n-1)+1, and
if a(n-1) is positive, a(n) = a(n-1)/2
Unfortunately I don't have subscripts at my disposal, so the function/sequence bleedover will have to suffice.
While it has yet to be proved, it is thought that the hailstone sequence converges to 1 for any starting number a(n). I was interested in the number of steps it took to reach one. For instance, starting number 2 obviously takes 1 step, and 4 takes 2. 3 takes 8 steps, while a starting number of 5 only takes 6. The graph then displays on the X-axis the starting number, and on the Y-axis the number of steps (for lack of a better word... perhaps "iterations"?) it takes to arive at one. I'll admit I stole the idea for such a graph from Wikipedia, but they only went up to 9,999, so I consider myself the victor, even more so if Excel could have more than 16384 columns, which my buddy pointed out is 2^14! He's a computer science major, so a more sophisticated graph may be forth coming.
On another note, a Saturday morning impromptu math class (a full 6 days of quality education for a 5 day price!) to learn about mathematical induction was scheduled. I am most excited!
Thursday, October 29, 2009
Random Prejudices
I find it very helpful to identify which of your prejudices are "random" and which have some basis behind them. For instance, a random prejudice of mine is a dislike of umbrellas. There is nothing wrong with the umbrella, in fact it is a generally good thing, I think all would conclude. I couldn't explain my reasoning behind my prejudice because I have absolutely none. Even still, every time the smallest amount of precipitation falls on campus I am utterly discouraged by the sight of so many umbrellas.
A non-random prejudice, a very just prejudice, is my dislike of same-sex bathrooms. Of course, I have been using a "same-sex" bathroom my whole life: few homes have facilities designated for women and men. But this is different. On every floor of the library, right next to the elevators there is a woman's restroom and a men's restroom, where the sexes can be with only their same kind, except on the second floor. For some reason the second floor is well-advertised as have two same-sex bathrooms. What's the point? The whole character of the bathroom is lost. There might have been a girl in my men's bathroom! The men's room should be a place where you can be away from the other sex! So, while I normally I abide on the third floor, reading St. Theresa's "Life", or on the fourth floor, studying Wheelock's Latin, yesterday I was on the second floor doing Calculus (learning why e^(Pi*i)=-1, in fact!) and I had to use the restroom. It was quite a dilemma for me, because I refused to support the misguided same-sex bathroom. Fortunately I had enough time to run up to the third floor, and entered the small, most perfect, men's restroom. I even had to wait for another fellow man (so much better than waiting for a girl) before I could relieve myself.
A non-random prejudice, a very just prejudice, is my dislike of same-sex bathrooms. Of course, I have been using a "same-sex" bathroom my whole life: few homes have facilities designated for women and men. But this is different. On every floor of the library, right next to the elevators there is a woman's restroom and a men's restroom, where the sexes can be with only their same kind, except on the second floor. For some reason the second floor is well-advertised as have two same-sex bathrooms. What's the point? The whole character of the bathroom is lost. There might have been a girl in my men's bathroom! The men's room should be a place where you can be away from the other sex! So, while I normally I abide on the third floor, reading St. Theresa's "Life", or on the fourth floor, studying Wheelock's Latin, yesterday I was on the second floor doing Calculus (learning why e^(Pi*i)=-1, in fact!) and I had to use the restroom. It was quite a dilemma for me, because I refused to support the misguided same-sex bathroom. Fortunately I had enough time to run up to the third floor, and entered the small, most perfect, men's restroom. I even had to wait for another fellow man (so much better than waiting for a girl) before I could relieve myself.
Friday, October 23, 2009
Excel
I found myself with nothing to do this afternoon, which is always an unsettling feeling, so I decided that I was going to make a liturgical calender using Excel in these stretches of time. Actuaries use Excel alot, and it's a pretty nifty program to boot (which is probobly why they use it), so I figured I ought to know how to use it.
Well, as you know, Easter falls on a different day each year (anywhere from March 22 to April 25 in fact). The calculation actually has to do with the lunar cycle: "Easter day is the first Sunday after the 14th day of the lunar month (the nominal full moon) that falls on or after 21 March (nominally the day of the vernal equinox)." Needless to say it gets quite difficult. The other liturgical dates aren't nearly as difficult: the First Sunday in Advent, which is comming upon us quickly, is 4 Sundays before Christmas.
So I figured that it'd be best to tackle Easter first. I used dateofeaster.net (conveniant...) to figure out how it was actually done. I used a different column to calculate the letters for each year and when I got the finished column (the date of Easter) I opened up another handy Microsoft product, Word, and used the "Replace" function to consolidate my formula. Unfortunately Excel cut me off at 9000 characters for my formula, so I needed to use two columns and hide one (oh, but I will have victory one day). My formula was so long because of the steps where you need to determine the day of the week and then do different things for each day; I did this by determining the day of the week, and then having a different "if" statement for each day, which takes 7 times the charachters I think it really ought to. I also found a more simple algorithm by a certain Carl Friedrich Gauss. But after quickly figuring out the First Sunday in Advent (which took a measly 350 characters in comparison!) I'm calling it quits for today.
Well, as you know, Easter falls on a different day each year (anywhere from March 22 to April 25 in fact). The calculation actually has to do with the lunar cycle: "Easter day is the first Sunday after the 14th day of the lunar month (the nominal full moon) that falls on or after 21 March (nominally the day of the vernal equinox)." Needless to say it gets quite difficult. The other liturgical dates aren't nearly as difficult: the First Sunday in Advent, which is comming upon us quickly, is 4 Sundays before Christmas.
So I figured that it'd be best to tackle Easter first. I used dateofeaster.net (conveniant...) to figure out how it was actually done. I used a different column to calculate the letters for each year and when I got the finished column (the date of Easter) I opened up another handy Microsoft product, Word, and used the "Replace" function to consolidate my formula. Unfortunately Excel cut me off at 9000 characters for my formula, so I needed to use two columns and hide one (oh, but I will have victory one day). My formula was so long because of the steps where you need to determine the day of the week and then do different things for each day; I did this by determining the day of the week, and then having a different "if" statement for each day, which takes 7 times the charachters I think it really ought to. I also found a more simple algorithm by a certain Carl Friedrich Gauss. But after quickly figuring out the First Sunday in Advent (which took a measly 350 characters in comparison!) I'm calling it quits for today.
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