# Category: Mathematics Tools

# Why Tau Trumps Pi – Scientific American

The article, which should be required reading for all advanced high school students, creates a tantalizing picture of how much easier certain fundamental concepts of trigonometry could be in an alternate universe where we use tau. For example, with pi-based thinking, if you want to designate a point one third of the way around the circle, you say it has gone two thirds pi radians. Three quarters around the same circle has gone one and a half pi radians. Everything is distorted by a confusing factor of two. By contrast, a third of a circle is a third of tau. Three quarters of a circle is three quarters tau. As a result of pi, Palais says, “the opportunity to impress students with a beautiful and natural simplification is turned into an absurd exercise in memorization and dogma.”

— Read on www.scientificamerican.com/article/let-s-use-tau-it-s-easier-than-pi/

# Secret Link Uncovered Between Pure Math and Physics | Quanta Magazine

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

— Read on www.quantamagazine.org/secret-link-uncovered-between-pure-math-and-physics-20171201/

The rational numbers include the integers and any number that can be expressed as a ratio of two integers, such as 1, –4 and 99/100. Mathematicians are particularly interested in rational numbers that solve what are called “Diophantine equations” — polynomial equations with integer coefficients, like *x*2 + *y*2 = 1. These equations are named after Diophantus, who studied them in Alexandria in the third century A.D.

# TAPS Resources: Mathematics Awareness Months-Sports is the THEME

April is Mathematics Awareness Month

The theme for 2010 is Mathematics and Sports

COD students can join in the fun by reading any of the following sports-related math articles here:

- Binomial Baseball “Programmable calculators can be used to play simulated baseball games. [] The use of random numbers to determine hits and outs introduces the student to the Monte Carlo method in a familiar context.”
- Designing A Baseball Cover “Problems in design, even those of a rather frivolous nature, can produce some very interesting mathematics. Consider the 130-year-old problem of designing the cover for a baseball. Early experimental work on this problem involved the freehand drawing of plane figures. We will use geometric insight and calculus to give a relatively easy solution of the problem in space. Next, a
**differential equation**will be derived that gives a mathematical solution with plane figures, in the style of the early efforts. Finally, we will see how well trial and error have worked, by looking at the cover design that is currently used in the manufacture of major league baseballs.” - Building Home Plate: Field of Dreams, or Reality? “In the moview Field of Dreams, Kevin Costner’s character, Ray Kinsella, considers building a baseball park in the middle of his cornfield. [] An assistant coach for my nine-year-old son’s baseball team, I was interesting to read in the official league rules the following specifications for home plate:”
- A Mathematician Catches a Baseball “In the game of baseball, what strategy does an outfielder employ to catch a fly ball? Recently, Michael McBeath and Dennis Shaffer, who are psychologists, and Mary Kaiser, a researcher at NASA, proposed a new model to explain how this task is accomplished. The model, called the linear optical trajectory (LOT) model, was developed and tested empirically by the three researchers, and it received national attention during the 1995 baseball season. In this paper, seeking to clarify what is written, we develop equations relating the motion of a fly ball to the motion of an outfielder utilizing the LOT strategy. In the process, we provide a mathematical foundation on which the LOT model can rest.”
- How To Make A Bank Shot Tennis Ball Paradox Geometric Series From Tennis

Source: MAM2010

# Electrical puzzle • Wires & Watts • Computer Chip Design • Circuit Design

Electrical puzzle

by Roger » Mon Feb 09, 2009 6:17 pm

Heres a puzzle you may have heard before which you can build as a simple electric circuit. First, the puzzle: a farmer is traveling to market with his cat, a chicken and some corn. He has to cross a river, and the only way to cross is in a small boat which can hold the farmer and just one of the three items he has with him. The problem is, he has to be very careful about what he chooses to leave behind at any time. If the cat and chicken are left alone, the cat will eat the chicken. If the chicken and the corn are left alone, the chicken will eat the corn. To solve the puzzle, you must show how the farmer can get himself and his three items across the river without losing any of them. The goal of this project is to design a simple electrical circuit that follows the puzzle. Youll need a 6 V battery, a flashlight bulb, a bulb holder, some connecting wire, and four toggle switches: 3 SPDT single-pole, double throw and 1 DPDT double-pole, double throw. Each switch represents one of the items: the farmer, the cat, the chicken and the corn you have to figure out which need to be SPDT switches and which one needs to be a DPDT switch. The switches are mounted on a small panel, in a horizontal row representing the river, which you can draw in. Each switch is labeled “Farmer”, “Cat”, “Chicken”, “Corn”. The circuit is to be designed so that if either of the problematic pairs cat-chicken, or chicken-corn are left alone on the same side of the river, the light bulb lights up, indicating an incorrect solution you can add a 6 V buzzer, too, if you like. Since the boat can hold only two items, players can use only two switches per “move”. Irwin Maths book, Wires and Watts: Understanding and Using Electricity has the solution Math, 1981, 67–70, but see if you can figure this one out on your own. The puzzle Ive got figured out but I am stuck on the wiring and cannot find an Irwin Math book.

via Science Buddies: “Ask an Expert” • View topic – Electrical puzzle.

# Digital Logic – Karnaugh Maps

Karnaugh Maps

Why Do You Need To Know About Karnaugh Maps?

Why Do You Need To Know About Karnaugh Maps?

Karnaugh Maps are used for many small design problems. It’s true that many larger designs are done using computer implementations of different algorithms. However designs with a small number of variables occur frequently in interface problems and that makes learning Karnaugh Maps worthwhile. In addition, if you study Karnaugh Maps you will gain a great deal of insight into digital logic circuits.

In this section we’ll examine some Karnaugh Maps for three and four variables. As we use them be particularly tuned in to how they are really being used to simplify Boolean functions.

The goals for this lesson include the following.

Given a Boolean function described by a truth table or logic function,

Draw the Karnaugh Mapfor the function.

Use the information from a Karnaugh Map to determine the smallest sum-of-products function.

What Does a Karnaugh Map Look Like?

A Karnaugh Map is a grid-like representation of a truth table. It is really just another way of presenting a truth table, but the mode of presentation gives more insight. A Karnaugh map has zero and one entries at different positions. Each position in a grid corresponds to a truth table entry. Here’s an example taken from the voting circuit presented in the lesson on Minterms. The truth table is shown first. The Karnaugh Map for this truth table is shown after the truth table.

# Adopt-a-Hydrant — Code for America

Adopt-a-HydrantOverviewAdopt-a-hydrant allows citizens to claim responsibility for shoveling out fire hydrants after heavy snowfall.

HTTP://ADOPTAHYDRANT.ORGCREATED BYERIK MICHAELS OBERCREATED FORCITY OF BOSTON

Adopt-a-hydrant allows citizens to claim responsibility for shoveling out fire hydrants after heavy snowfall.

SUMMARY

Live http://adoptahydrant.orgCodebase https://github.com/codeforamerica/adopt-a-hydrantEnvironment Ruby on Rails with Postgres databaseRedeploy Use the code in the Github repository or DOBT’s hosted Adopta.Contact us to deploy this appIn the midst of winter snowstorms, buried hydrants cause dangerous delays for fire fighters. But having City of Boston employees check and clear thousands of hydrants would be a timely, costly and burdensome process.Adopt-a-Hydrant lets governments look to community members for help. This map-based web app allows individuals, small businesses and community organizations to volunteer in shoveling out specific hydrants.

# Computer Programming Is a Trade; Lets Act Like It – WSJ

The most intensive schools, like Seattle-based Code Fellows, are so sure they can get students work they will refund a students tuition—$12,000 for 16 blitzkrieg weeks to get a person from zero to trained—if that person doesnt get a job.Whats going on here isnt complicated: There is an enormous mismatch between the supply and demand for computer programmers. The U.S. Bureau of Labor Statistics projects that by 2020, one million programming jobs in the U.S. will go unfilled. And traditional institutions, which largely treat introductory computer-science classes as barrier courses designed to weed out all but the most committed students, are demonstrably not meeting the need. This year, the University of Washington could accommodate only a quarter of the qualified students who applied to its computer science major. And this is happening at schools across the country, most of which have seen hockey-stick growth in applications to both be computer-science majors and to take individual courses in recent years.Fortunately, it turns out that a computer-science degree isnt necessary to get a job in programming. Fourteen percent of the members of some teams at Google dont have a college degree, and 67% of the programming jobs in the U.S. are at nontech companies where other kinds of industry experience are more likely to be valued.Computer programming, in other words, has become a trade. Like nursing or welding, its something in which a person can develop at least a basic proficiency within weeks or months. And once budding coders learn enough to get their first jobs, they get onto the same path to upward mobility offered to their in-demand, highly paid peers.Take Facebook FB -0.87% : The first thing that happens to a new engineer there is six weeks of intensive classes, many of which are—you guessed it—programming classes. This is in part because university courses in computer science favor theory over programming, which is a mishmash of skills ranging from practical knowledge of in-vogue programming languages to how to work on projects that involve dozens of other programmers and thousands or even millions of lines of code.Coding schools, online and otherwise, let everyone from recent high-school graduates to career switchers skip straight to the part where they learn how to make the things companies actually care about—websites, services and apps.That is not to dismiss the value of a computer-science degree or even a college education—if a student can afford it. But now that student-loan debt in the U.S. has swelled to a record $1.2 trillion, many clearly cannot.

via Computer Programming Is a Trade; Lets Act Like It – WSJ.

# Is Coding the New Literacy? | Showing Kids the Why of Learning to Program

Adopt-a-Hydrant after cutbacks slashed his budget, and now Honolulu has Adopt-a-Siren, where volunteers can sign up to check for dead batteries in tsunami sirens across the city. In Oakland, its Adopt-a-Drain.

Sounds great, right? These simple software solutions could save lives, and they were cheap and quick to build. Unfortunately, most cities will never get a CFA team, and most cant afford to keep a stable of sophisticated programmers in their employ, either. For that matter, neither can many software companies in Silicon Valley; the talent wars have gotten so bad that even brand-name tech firms have been forced to offer employees a bonus of upwards of $10,000 if they help recruit an engineer.In fact, even as the Department of Labor predicts the nation will add 1.2 million new computer-science-related jobs by 2022, were graduating proportionately fewer computer science majors than we did in the 1980s, and the number of students signing up for Advanced Placement computer science has flatlined.Code.orgTheres a whole host of complicated reasons why, from boring curricula to a lack of qualified teachers to the fact that in most states computer science doesnt count toward graduation requirements. But should we worry? After all, anyone can learn to code after taking a few fun, interactive lessons at sites like Codecademy, as a flurry of articles in everything from TechCrunch to Slate have claimed. Michael Bloomberg pledged to enroll at Codecademy in 2012. Twelve million people have watched a video from Code.org in which celebrities like NBA All-Star Chris Bosh and will.i.am pledged to spend an hour learning code, a notion endorsed by President Obama, who urged the nation: “Dont just play on your phone—program it.”

So you might be forgiven for thinking that learning code is a short, breezy ride to a lush startup job with a foosball table and free kombucha, especially given all the hype about billion-dollar companies launched by self-taught wunderkinds with nary a mention of the private tutors and coding camps that helped some of them get there. **The truth is, code—if what were talking about is the chops youd need to qualify for a programmer job—is hard**, and lots of people would find those jobs tedious and boring.

But lets back up a step: What if learning to code werent actually the most important thing? It turns out that rather than increasing the number of kids who can crank out thousands of lines of JavaScript, **we first need to boost the number who understand what code can do**. As the cities that have hosted Code for America teams will tell you, the greatest contribution the young programmers bring isnt the software they write. Its the way they think. Its a principle called “computational thinking,” and knowing all of the Java syntax in the world wont help if you cant think of good ways to apply it.

# The Guy Behind Garbage Pail Kids Has Been Cartooning With Code for 20 Years | Design | WIRED

John Pound lives in Eureka, California. He’s either 62 or 63–he can’t remember at the moment–and he’s been a cartoonist his whole life. The first half of his career was traditional,

insofar as any career in weirdo art and underground comics can be traditional. He sketched and inked and colored by hand. He made the annual pilgrimage to Comic-Con, back in the days where it was still concerned with comics. In 1984, he collaborated with comics legend Art Spiegelman on the first run of Garbage Pail Kids cards for Topps, painting 40 gross characters in 40 exhausting days. But in the late 1980s, the purchase of his first computer, an Amiga, set Pound’s artistic pursuits on a slightly different course. He started checking out other people’s computer art and got to wondering what his new machine could do for a cartoonist. Eventually, he became smitten with the idea of creating a program that could automatically generate comics for him. The dream has kept him busy for the better part of three decades. Today, he’s generating striking, randomly generated compositions by the hundreds, none of which look anything like what the art we’ve come to expect from computer code.

via The Guy Behind Garbage Pail Kids Has Been Cartooning With Code for 20 Years | Design | WIRED.