# Altermundus: Parallel and Perpendicular Lines

I've added some more information on the Altermundus tkz-euclide package; it's posted on the Points, lines, rays and segments page. The new material deals with the macros for creating parallel and perpendicular lines as well as getting the point of intersection for 2 lines. The code for both examples (along with commentary) is posted online for you to download and modify to suit your needs.

Here are some stories that caught my eye this week:

• ZeroHedge on the desperate financial shape of Detroit public schools. "Case in point: today we learn that Detroit's public schools have officially reached their borrowing limit which means absent some manner of intervention from the state government, the district will run out of cash by April...."DPS is finally on the brink," State Treasurer Nick Khouri told lawmakers today. “When they run out of cash, sometime in the spring or early summer, without legislative interaction, they will have payless paydays," he warned....Each year, the district spends $70 million more than it brings in in revenues, but a bankruptcy would result in 12 months of "chaos," Khouri cautioned." • The Herald Tribune has a piece on the educational games that "educators" play, "The vast majority of states have adopted Common Core academic standards, but individual states are still setting different definitions of "proficient" on annual math and reading tests, according to a new study. And in many states, the study says, annual tests set a significantly lower bar for "proficient" than the National Assessment for Educational Progress, or NAEP, a national exam that is administered every two years to a sample of students in the fourth and eighth grades.". Because when "professionals" know they are failing at their job there is always statistics to make it less obvious. • TownHall reflects on how Common Core cost Jeb! the election: "Exactly one year ago, before he announced that he would be running for president, Trump was asked on Hugh Hewitt's radio talk show: "What does Donald Trump think about Common Core?" He replied, "Well, first of all, I think it's going to kill Bush."...One year later, it's clear that Trump was right: not only that it's "ridiculous" for "people in Washington" to be setting curriculum and standards for "what you're going to be studying" -- but he was equally right to foresee that Common Core would "kill" any chance of returning the Bush family to the White House....As Common Core became toxic, Jeb Bush made a too-little, too-late attempt to rebrand the same ideas under a new name. " • EAGNews on the potential drugging of a teacher at school, "Police are investigating at the school after the teacher developed “unusual symptoms that required him to seek medical attention” last Tuesday....“During a school day last week, one of our employees consumed a beverage that may have been laced with an unknown substance,” Smithville Superintendent Todd Schuetz wrote in a letter to parents." This isn't the world you grew up in. • File this under "what's the world coming to?": according to RT, "Teens in the US state of New Mexico have been officially allowed to keep themselves busy sexting – sending or receiving sexually explicit messages, images through e-means, particularly between cell phones – without fear of paying the price and going to jail." • TheRegister reports that "The Chicago Public Schools district has become the first in the nation to make computer science training a requirement for high school graduation." Great idea but I'm more than a little surprised that California wasn't able to have a school district accomplish this. • NBCnews on the long overdue termination of Melissa Click, "Melissa Click made national headlines when a video of her attempting to kick out a campus reporter during protests at the University of Missouri went viral. In the video, Click can be heard yelling "I need some muscle over here!" as she tries to boot the journalist."The board believes that Dr. Click's conduct was not compatible with university policies and did not meet expectations for a university faculty member," Pam Henrickson, chair of the University of Missouri Board of Curators, said in a statement."...Click was branded a traitor to her profession by some and in January, she was charged with assaulting Schierbecker. She apologized, and cut a deal with prosecutors last month that kept her out of jail" • EAGNews reports on a kerfuffle at University of South Carolina: "Student Ross Abbott created an outdoor First Amendment display highlighting kinds of speech that had been subjected to censorship... Abbott even took the extra step of actually obtaining prior approval from administrators. But that did not stop several of his fellow students from filing complaints....Even though administrators had approved the display, Abbott was still given official notice that he was being investigated for discrimination. He was eventually called before the Office of Equal Opportunity Programs and made to answer for each and every poster he had displayed....Since the university did not respond to Abbott's request to have the complaint expunged from his academic record—and because USC gave no indication that it understood Abbott's speech was constitutionally protected—he has filed suit." # LaTeX: Geometry proof template The latest addition to the website is a$latex \LaTeX$file that can serve as a template for proofs in geometry. I've posted it on the Handouts page. You'll need to download both the .tex file and the accompanying figure ProofPic.pdf for the document to compile properly. Just replace ProofPic.pdf with your picture and modify the statements and reasons and you'll save yourself a lot of time creating nice looking proofs. Here are some stories that caught my eye this last week: • The untimely death of Supreme Court Justice Scalia is expected to impact U.S. education. According to Global Research, "Scalia’s timely departure implies that the landmark union case “Friedrichs vs. California Teachers Association” will be a 4-4 stalemate, meaning the pro-labor status-quo prevails. As they cheer the last minute pardon unions shouldn’t forget they’re still on death row. The solace is temporary." • Huffington Post reports on the growing resistance to Common Core: "John King the new Acting U.S. Secretary of the Department of Education (DOE)...said, "And finally--we at the state level and our colleagues at the federal level need to own up to the unintended consequences of our policies -- from narrowing of the curriculum to an overemphasis on testing." Incredibly, he said we are going forward. (King and Obama both send their children to private, progressive schools).....Obama, King, and Congress keep ignoring a major nine-year study, "Incentives and Test-Based Accountability in Education," released in 2011 by the prestigious and highly respected National Academies of Sciences' National Research Council. It studied No Child Left Behind and 14 other test-based accountability programs. It found few or no gains in student achievement and gaming of the test scores by the states...."There is evidence of attempts to increase scores in ways that are completely unrelated to improving learning. The attempts included teaching test-taking skills, excluding low performing students from tests, feeding students high-calorie meals on testing days, providing help to students during tests, and even changing student answers on tests after they were finished," (Pages 62-3).". Educators who don't educate and people in charge of making decisions on public education who won't send their own children to public school. Perhaps the quickest way to fix things would be to require education policy makers to send their own children to public school?!? • The Wichita Eagle with a piece on "Kansas lawmakers are making another attempt at repealing Common Core standards, a measure that could affect and possibly do away with Advanced Placement classes and International Baccalaureate programs....The Kansas State Department of Education has estimated the development of new standards would take two years and cost$9 million. Opponents say the financial impact could be much higher, particularly if districts would be required to replace Common Core-aligned textbooks and other materials." Common Core apologists are in defensive mode saying Common Core is just a set of standards, and Kansas is looking at developing new standards at the cost of 9 million dollars. You have to ask yourself why should standards (e.g. a student will learn towichita eagle anti-common core measure kansas multiply two 3 digit numbers) cost so much at the state and national level; and then you'll see why Common Core isn't just a set of standards.
• I've seen enough cases where teacher awards go to teachers that shouldn't get it but this EAGNews story is at a different level: "Police contend Hankins Middle School teacher Jeremiah Hunter kept a framed picture of a former 16-year-old female student on his bedside table. They said 39-year-old’s phone screensaver is also an image of the girl. The revelations are among a hoard of “disturbing evidence” collected at Hunter’s home that also included cell phones, computers, and other items that illustrates a “level of obsession” with his alleged teen victim, WTVM reports."
• The Press-Telegram with a story to awaken the inner mathematician in you: "Jim Stein of Redondo Beach, a 30-year math teacher at CSULB, has written his first nonfiction book, “LA Math,” a crime-romance story where characters use math to solve crimes."

# Sagetex: Rational Functions 3

This week I've added another example to the Sagetex: Functions page. This one is quite similar to the previous example: there are two vertical asymptotes and one horizontal asymptote. But in this case the horizontal asymptote is a line other than y=0.

Here are some stories that caught my eye over the last week:

• The Atlantic has an article on how, despite America's poor showing in math, the number of students excelling in math is growing. But wait for it..."Parents of students in the accelerated-math community, many of whom make their living in stem fields, have enrolled their children in one or more of these programs to supplement or replace what they see as the shallow and often confused math instruction offered by public schools, especially during the late-elementary and middle-school years."
• Sott.net quoting the Daily Caller, "In the syllabus for her "Creativity In Context" class — a required course for any student pursuing a minor in Innovation — UF professor Jennifer Lee informs students of her four paragraph long classroom "communications policy" that she says will enforce "ethical conduct" in the classroom....The policy mandates that students "[s]peak in a way that does not make assumptions about others based on "norms", stereotypes, or one's own identity or experience."...The syllabus explains that this means replacing the words "boyfriend"/"girlfriend" with the more inclusive "partner" or "significant other." The rule applies to conversations about married couples too: saying "husband" or "wife" is forbidden. Even the words "mom" and "dad" have a more "inclusive" alternative — students are told to use the word 'family" instead.". Around fifty years ago getting a college degree wasn't essential. People learned "the basics" by the end of high school and college was for advanced studies. Now, it seems that typically students are graduating high school unready for college but then go on to college because "you have to" but lacking the education end up taking courses like...well like Creativity in Context. So now, at the end of college they have an enormous debt burden, no real skills, and are learning cr@p. How did education get to this?
• Good news, class! MedicalNewsToday reports "A math test a day keeps the weight away, by activating brown fat"
• Who's running the SAT anyway? They've lost a lot of business to ACT because of poor test design. So they've redesigned the test and it looks like they made it worse. From the NY Times: "Chief among the changes, experts say: longer and harder reading passages and more words in math problems. The shift is leading some educators and college admissions officers to fear that the revised test will penalize students who have not been exposed to a lot of reading, or who speak a different language at home — like immigrants and the poor.....College Board officials said the new test was devised to satisfy the demands of college admissions officers and high school guidance counselors for an exam that more clearly showed a connection to what students were learning in school. " What better way to test someone's math skills than by putting a heavy emphasis on reading and vocabulary....winner: ACT.
• the74million.org with a piece on a petition in California to get high school credit taking computer classes. Great idea, just don't cut math classes to do it (unless it's statistics...because statistics isn't really math) and get discrete math into the curriculum at the same time.
• Yet another school shooting. RT.com on two teenagers killed this week in an "apparent murder suicide" at an Arizona public school: "Initial reports described the victims as “two teenagers,” but offered no details. One KNXV-TV source said that two female students may have got into an “altercation” at the cafeteria, which ended with gunshots."

# Sage Interact: Taylor Polynomials

I've added another Sage Interact to the Python/Sage page. The text can be copied into any Sage Cell Server, like the three that are on the Sage Sandbox page. Just press "Evaluate" and the Sage Interact appears; This Interact allows you to generate Taylor polynomial approximations for a function about some center. It's a little unpolished because you set the function to graph, the center of the expansion, the width (xrange shown is 2*width) and the minimum and maximum y values for the figure in the code itself. The resulting Sage Interact is programmed to handle the Taylor polynomials of degree 1 through 7. Simply click the boxes to display which  the polynomials you want to see. The screenshot above shows the function $latex e^{x}$ with center 1 having a dot on it. Of course you can modify the size or not plot the point if you find it too distracting.

Don't overlook the "TaylorPoly.pdf" in the bottom left.

Right click on the link to download a pdf of the figure for your own use. This is a quick and easy way to generate examples for, say, a Powerpoint beamer presentation.

I also need to mention that Detlef Reimers, the author of the lapdf package for LaTeX, left some comments. One is on the Common Core Questions page where he shares his philosophy behind the lapdf package which and states, "The audience for such a packet full of math, programming utilities (loops) and many complex drawing commands - directly based on the fore runner of PDF, PostScript - would generally be the scientific orientated people.". I agree. If you haven't tried the package then you definitely need to. My complaint at the time was the lack of good documentation--the package has a lot to offer but you have to be willing to puzzle through the details on how to make things work. The good news is that the package is currently undergoing an update which will provide some more documentation and fix the problems I noticed with ellipses. In a second comment, at the bottom of the lapdf packge post, Mr Riemers mentions that lapdf has some ability to draw chess diagrams--you can go to the links and check out some of what he's working on. I'll be looking forward to seeing the the new version of lapdf show up on CTAN.

Here are some stories that caught my eye over the last week.

• Hikaru Nakamura won the 2016 Tradewise Gibraltar Masters chess tournament on tiebreaks over MVL; both players had 8/10. Nakamura bested MVL 3-2 in speed chess.
• John Cleese of Monty Python fame was in a ZeroHedge article, "John Cleese says political correctness has gone too far, especially on America's college campuses, where he will no longer go to perform...Cleese, having worked with psychiatrist Robin Skynner, says there may even be something more sinister behind the insistence to be always be politically correct.
"If you start to say we mustn't, we mustn't criticize or offend them then humor is gone. With humor goes a sense of proportion. And then as far as I'm concerned you're living in 1984.""
Serious words from a funny man.
• EAGNews with headlines that over 15,000 Chicago school employees make over \$100,000 a year. "So what is the overall record of student learning and achievement in the Chicago district? Absolutely awful. “Four out of ten CPS freshmen don’t graduate,” reported HuffingtonPost.com in 2014. “Ninety-one percent of CPS graduates must take remedial courses in college because they do not know how to do basic math and other schoolwork. Only 26 percent of CPS high school students are college-ready, according to results from ACT subject-matter tests.“Education should be the great equalizer; but in Chicago, public education is more of a holding cell than a launch pad.”" Bad education+expensive price tag+ lack accountability =waste of money.
• The Washington Post reports there is a noticeable performance difference between students taking Common Core with a computer versus those using pencil and paper, "...about one in five took the exam with paper and pencil, and those students — who tested the old-fashioned way — tended to score higher than students who took the tests online...It’s not clear whether the score differences were due to the format of the testing, or due to differences in the backgrounds of the students who took the two different types of test, according to the Feb. 3 Education Week report. But the publication reported that in some cases the differences were substantial enough to raise concerns about whether scores on the exam — the Partnership for Assessment of Readiness for College and Careers test — are valid and reliable enough to be used for teacher evaluations or school accountability decisions." Did you catch that? The differences are, apparently, valid and reliable enough to gauge the student but not the teacher or school.
• I'd been ignoring this story until the The Columbian piqued my interest with a flashier headline (linking the Babylonians with calculus) for a reprint of a Washington Post piece, "The astronomers of Babylonia, scratching tiny marks in soft clay, used surprisingly sophisticated geometry to calculate the orbit of what they called the White Star — the planet Jupiter. These tablets are quite incomprehensible to the untrained eye. Thousands of clay tablets — many unearthed in the 19th century by adventurers hoping to build museum collections in Europe, the United States and elsewhere — are undeciphered." Until a key breakthrough, "... The calculations merely describe Jupiter’s motion over time as it appears to speed up and slow down in its journey across the night sky. Those calculations are done in a surprisingly abstract way — the same way the Oxford mathematicians would do them a millennium and a half later. “It’s geometry, which is itself old, but it’s applied in a completely new way, not to fields, or something that lives in real space, but to something that exists in completely abstract space,” Ossendrijver said. “Anybody who studies physics would be reminded of integral calculus.”Which was invented in Europe in 1350, according to historians.""