EppsNet Archive: Math

Competitive Programming: POJ 1905 – Expanding Rods

Description When a thin rod of length L is heated n degrees, it expands to a new length L’=(1+n*C)*L, where C is the coefficient of heat expansion. When a thin rod is mounted on two solid walls and then heated, it expands and takes the shape of a circular segment, the original rod being the chord of the segment. Your task is to compute the distance by which the center of the rod is displaced. Input The input contains multiple lines. Each line of input contains three non-negative numbers: the initial lenth of the rod in millimeters, the temperature change in degrees and the coefficient of heat expansion of the material. Input data guarantee that no rod expands by more than one half of its original length. The last line of input contains three negative numbers and it should not be processed. Output For each line of input, output one… Read more →

Math Skills of the Average American

My son was home for a visit this past weekend. After a family dinner at the Irvine Spectrum, we found ourselves in a women’s clothing store with a sale going on: 40% Off All Merchandise + An Additional 10% Off. My son said to me, “Isn’t that just 46 percent off? They probably want it to sound like you’re getting 50 percent off.” “You can’t underestimate the math skills of the average American,” I said. Right on queue, a woman said to her husband, “Why don’t they just say 50 percent off?” “Exactly,” he said. Read more →

Teaching Computer Science: Next Year’s Teacher

I’m volunteering a couple mornings a week in an AP Computer Science Principles class for the upcoming school year . . . Schools are adding more CS classes and, almost without exception, retraining in-service teachers to teach them, rather than hiring people with knowledge and experience in the field. I met with the teacher today to do some upfront planning. At one point, he was calculating how many printouts we’d need for 6 groups of 4 students each . . . “Let’s see,” he said, “6 times 4 is 20 . . .” If you think that’s funny, guess what class he normally teaches: accounting. “Are you going to write that?” someone asks me. “Does he know you have a website?” “I don’t know what he knows or doesn’t know. Except he doesn’t know what 6 times 4 is.” Read more →

Competitive Programming: POJ 1426 – Find The Multiple

Description Given a positive integer n, write a program to find out a nonzero multiple m of n whose decimal representation contains only the digits 0 and 1. You may assume that n is not greater than 200 and there is a corresponding m containing no more than 100 decimal digits. Input The input file may contain multiple test cases. Each line contains a value of n (1 <= n <= 200). A line containing a zero terminates the input. Output For each value of n in the input print a line containing the corresponding value of m. The decimal representation of m must not contain more than 100 digits. If there are multiple solutions for a given value of n, any one of them is acceptable. Sample Input 2 6 19 0 Sample Output 10 100100100100100100 111111111111111111 Link to problem Solution below . . . Read more →

Competitive Programming: POJ 2084 – Game of Connections

Description This is a small but ancient game. You are supposed to write down the numbers 1, 2, 3, . . . , 2n – 1, 2n consecutively in clockwise order on the ground to form a circle, and then, to draw some straight line segments to connect them into number pairs. Every number must be connected to exactly one another. And, no two segments are allowed to intersect. It’s still a simple game, isn’t it? But after you’ve written down the 2n numbers, can you tell me in how many different ways can you connect the numbers into pairs? Life is harder, right? Input Each line of the input file will be a single positive number n, except the last line, which is a number -1. You may assume that 1 < = n Read more →

Competitive Programming: POJ 2242 – The Circumference of the Circle

Description To calculate the circumference of a circle seems to be an easy task – provided you know its diameter. But what if you don’t? You are given the cartesian coordinates of three non-collinear points in the plane. Your job is to calculate the circumference of the unique circle that intersects all three points. Input The input will contain one or more test cases. Each test case consists of one line containing six real numbers x1,y1,x2,y2,x3,y3, representing the coordinates of the three points. The diameter of the circle determined by the three points will never exceed a million. Input is terminated by end of file. Output For each test case, print one line containing one real number telling the circumference of the circle determined by the three points. The circumference is to be printed accurately rounded to two decimals. The value of pi is approximately 3.141592653589793. Sample Input 0.0 -0.5… Read more →

Are You Smarter Than a Common Core Algebra Student?

You can test your Common Core algebra skills against a 5-question sample test courtesy of the the New York Times. For all the controversy about Common Core, the questions seem pretty basic even for a person with an aging brain (I frigging CRUSHED it with a perfect 5 out of 5), the one exception being a graphing problem that should separate the mathematicians from the wannabes. How hard is New York's high school algebra exam? 5 questions to test your math skills. Posted by The New York Times on Monday, November 30, 2015 Read more →

If Math Was Taught Like Science

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When is Diversity Not a Dilemma?

I just read yet another brief — Solving the Diversity Dilemma — regarding lack of diversity in the STEM workforce. If members of Group X are underrepresented in some professions, they must be overrepresented in others. For example, I used to work with a nursing organization . . . women far outnumber men in nursing but for the five years I worked there I never heard anyone talk about the shortage of men in nursing being a dilemma, crisis, etc., or suggesting that anything be done to change it. I work in a STEM field. It’s a good job for me but not for everyone. My son (age 21) for example, never showed any interest in it and I don’t think he’ll be any less happy in life because he’s not working in STEM. There are pluses and minuses like any other profession. Simple but possibly valid explanation for STEM… Read more →

A Mega Millions Lottery Ticket is a Good Investment

Mega Millions uses 75 numbers for the first five selections and 15 numbers for the Mega ball. The number of unique combinations of five numbers selected from a pool of 75 is Multiply that times 15 possibilities for the Mega ball and the odds of winning come out to 1 in 258,890,850. BUT THE CURRENT MEGA MILLIONS JACKPOT IS OVER $350 MILLION! Any time you can get 350 million to one odds on a 258 million to one bet, you’ve got to take it. Read more →

The Hardest Available Challenge

One of my colleagues at work has a son in 6th grade. She’s trying to figure out which math class to put him in for 7th grade. Working backward, we know that “normal” kids take Algebra I in 9th grade, the smarter kids take Algebra I in 8th grade, and the smartest kids take Algebra I in 7th grade. Placement depends on how a kid scores on the math placement test. My co-worker’s concern is if her kid gets a top score on the placement test and he’s eligible to take Algebra I in 7th grade, does she want him to do that, or to wait till 8th grade? If he takes Algebra I in 7th grade, that would mean he’d be taking the hardest math classes all through high school. Would it be better from a college admission standpoint to take easier classes and get all A’s, or take… Read more →

We’re Still Smarter Than You Are

Teens from Asian nations dominated a global exam given to 15-year-olds, while U.S. students showed little improvement and failed to reach the top 20 in math, science or reading, according to test results released Tuesday. — Why Asian teens do better on tests than US teens – CSMonitor.com Why am I not shocked by that? Because Americans on the whole are dumb and lazy. We have lots of dumb, lazy parents raising dumb, lazy kids. The average American kid doesn’t compare well academically to the average kid in an Asian country where academics and hard work are valued, or to the average kid from a small, homogenous European country where it’s easier to get everyone pulling in the same educational direction. The U.S. is a big, diverse country and the average academic results are pulled down by a lot of dummkopfs. But still, the smartest people in the world are… Read more →

Fast Work

A junior high school math teacher posted this on Facebook: That makes perfect sense to me. Work gets done a lot faster if the results don’t have to be correct. Thus spoke The Programmer. Read more →

Screw Economics

One of the classes I’m taking on Coursera is Principles of Economics for Scientists, taught by Prof. Antonio Rangel at Cal Tech. First of all, it’s a great class. Rangel has a real passion for the material and he’s provided extra resources to accomodate online students, many of whom probably don’t have the math background of the average Cal Tech student. He’s from Madrid, so his pronunciations and mannerisms are different, like the gesture below, which I captured from one of the video lectures. He was explaining how something or other would increase our understanding of economics and he punctuated the word “understanding” by pointing at his head with two fingers. I don’t know what this gesture means in Spain, or if it means anything at all. Probably he knows what it means in America, but as I said, he’s passionate about the material and I think he loses himself… Read more →

“Keep it Simple,” Nobel Prize Winner Advises

I soon was taught that [Linus] Pauling’s accomplishment was a product of common sense, not the result of complicated mathematical reasoning. Equations occasionally crept into his argument, but in most cases words would have sufficed. The key to Linus’ success was his reliance on the simple laws of structural chemistry. The -helix had not been found by only staring at X-ray pictures; the essential trick, instead, was to ask which atoms like to sit next to each other. In place of pencil and paper, the main working tools were a set of molecular models superficially resembling the toys of preschool children. We could thus see no reason why we should not solve DNA in the same way. All we had to do was to construct a set of molecular models and begin to play — with luck, the structure would be a helix. Any other type of configuration would be… Read more →

Tips for Test Takers

My son has a math test today. He was up till 3 a.m. studying for it. In my experience, a positive mindset is essential to successful test-taking, so on the drive to school, I give him a piece of advice. “Walk into the classroom,” I say, “look at the teacher and lay down a challenge, like ‘Let’s do it.’” “It’s not her test,” the boy says. “What does that mean?” “It means every class takes the same test — Schneider, D’Antonio . . .” “THAT DOESN’T MATTER,” I say. “The important thing is to lay down the challenge. ‘Stop bitin’ on my styles.’ Granted, that one doesn’t make any sense, but it gives you the positive mental framework that you need for mathematical success.” Read more →

Things I Love to Do on a Hot Summer Evening

My son’s going into 11th grade next week. He’s got a couple of honors classes, a couple of AP classes, Spanish 3 and a music class. It looks like a very tough schedule to me — he’s also got college entrance exams this year — but that’s where his academic history has brought him and he says he wants to do it. One thing I didn’t know about AP classes is that they start giving kids assignments during summer vacation. He’s working on ’em right now! He asked me for a little help on the physics assignment so I get to do two things I love to do on a hot summer evening: sip premium tequila on ice with a lime, and solve problems like this: A kangaroo jumps to a vertical height of 2.7m. How long is it in the air before returning to Earth? Oh I’m in heaven! Read more →

Americans are Mathematically Illiterate

If anyone ever told you there’s no reason to learn math in school, they are absolutely right! Americans are so mathematically illiterate that you’re better off learning to speak Klingon if you want anyone to understand you. I wish I had a dollar for every time I’ve walked through a mathematical demonstration of some concept and gotten back a reply like “Well I don’t see any reason why . . .” or “Let’s have a meeting to discuss that.” God, it’s painful. If you’re still in school, don’t bother learning any more math than you absolutely have to. It’ll just come back to haunt you. Read more →

Homework Follies

My son just came downstairs for a visit . . . “‘What’s due tomorrow?’” he says in his Dopey Dad voice. Then back in his normal voice: “Math and Spanish. (Dopey Dad voice) ‘Are they done yet?’ (Normal voice) Spanish is done. I still have a little bit of math. (Dopey Dad voice) ‘Do you need me to check anything?’ (Normal voice) No.” Now he’s waiting for a reaction from me, which he’s not going to get. “I just did your job for you,” he says. “Thanks!” Read more →

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