Altermundus: creating simple geometric diagrams

I've added an example to the page on creating lines and rays with the Altermundus package. The additional information is posted here. Start with a typical geometric diagram you might need to construct in high school mathematics.

TrigDiag1I'm calling the diagram "simple" because it consists of line segments, angle markings and text. In order to create the lines, you need 2 points. Therefore, when you look at the diagram you should see 9 points are needed.


I take the bottom left point to be the origin but that isn't required. The building on the left is made up of 4 points:


The building on the right has 5 points:


Once you have the 9 points defined you create the line segments. In addition to \tkzLabelSegment there is \tkzDrawPolygon. The \tkzDrawPolygon takes 3 or more points and creates polygon defined by them. The building on the left and right are \tkzDrawPolygon(A1,A2,B2,B1) and \tkzDrawPolygon(D1,D2,E2,E1), respectively. The dashed lines are created:

\tkzDrawSegments[dashed](B2,H B2,D2 B2,D1)

Be careful here! Note that there is a space after every 2 vertices. Putting a comma between them causes an error. After that the \tkzLabelSegment is used to get text.
\tkzLabelSegment[right=3pt](B1,B2){$100$ ft}

and finally the angles are marked and labelled.

\tkzLabelAngle[pos = 0.75](H,B2,E2){$42^{\circ}$}
\tkzLabelAngle[pos = 1.0](E1,B2,H){$20^{\circ}$}

Note the is a special command to create the right angle mark.

By breaking down a simple geometric diagram into the points needed to create the lines, you can easily decompose the picture into pieces that can be plotted with the macros mentioned. Define the points, create the lines, and add the text. See the page on creating lines and rays with the Altermundus package for the complete file to create the diagram.

Sagetex: derivative as a limit

LimDQI've added another problem to the Sagetex: Limits page. Find the derivative of quadratic function using the limit of a difference quotient. The screenshot is above.

Several stories caught my eye recently:

  1. William Stein, the driving force behind Sage, reports on a, "major 3d update. Print worksheets with embedded 3d graphics. Pan with alt/command. Plots persist between refreshes.". More details can be found here.
  2. The Washington Post has a piece about an "award winning" principal who used to support Common Core and is now opposed to it. She writes about the "Four Common Core 'Flim-Flams'".
  3. Common Dreams reports: "Hundreds of students from high schools across Colorado's Jefferson County school district walked out of classes on Monday, Tuesday, and Wednesday this week, protesting attempts by rightwing members of the school board to amp up what they consider the "positive aspects of the United States and its heritage" within the district's history curriculum while minimizing focus on more progressive aspects of history such as people's movements, the history of struggle, and "social strife."". The article says, "that plan would look at Advanced Placement history courses to make sure materials "promote citizenship, patriotism, essentials and benefits of the free-market system, respect for authority and respect for individual rights" and don't "encourage or condone civil disorder, social strife or disregard of the law."" A passage from a piece on the Breitbart website gives a student opining, "...the nation's foundation was built on civil protest, "and everything that we've done is what allowed us to be at this point today. And if you take that from us, you take away everything that America was built off of."".
  4. This hasn't gotten much publicity: reports, "A secret program to monitor students' online activities began quietly in Huntsville schools, following a phone call from the NSA, school officials say.". According to the school officials they were alerted to a student making threats on Facebook. "The NSA, a U.S. agency responsible for foreign intelligence, this week said it has no record of a call to Huntsville and does not make calls to school systems.". So now Huntsville City Schools are looking at social media sites for gangs, guns, and threats of violence. One school official says, ""There was a foreign connection," said Wardynski, explaining why the NSA would contact Huntsville schools. He said the student in Huntsville had made the online threats while chatting online with a group that included an individual in Yemen.". But it's not just Huntsville. The article continues, "A company called Geo Listening watches social media for school districts including Glendale, Calif. Their web site reads: "Geo Listening's unique monitoring service will process, analyze and report the adverse social media from publicly available student posts... We align our reporting criteria with existing school district procedures and board policy as they relate to student conduct & safety."".

Sagetex: Dartboards and tree diagrams

CombDartsI've added another problem to the Sagetex: Combinatorics/Probability page: "Three darts are thrown at the dartboard. A score is given for each region where the dart lands and the total score is just the sum of the $3$ dart scores. Assume all three darts hit the dartboard. How many different total scores are there? Enumerate them with by drawing a tree diagram."

It's a problem that's illustrates how a tree diagram can be used to organize the solution in a way that anyone can easily check the answer. Typesetting the tree diagram made this a a time consuming problem to create. But the work is done now and the code can be downloaded for you convenience.

Here are some stories that caught my eye recently:

  • Ben Swann alerts us to a "zero tolerance" policy to the extreme.  In Teen Suspended After School Claims Notebook is "Drug Possession" we learn "...a teenager was punished with a lengthy suspension after teachers discovered her folder which contained stories with references to marijuana use." . Her suspension of 10 days was for "...“possession of a controlled substance” despite no drug testing and no drugs in Krystal’s possession". Her written account is considered  possession, apparently, "...although the district’s drug policy posted online provides no specific definition of paraphernalia".
  • CBS San Francisco reports on how outrageous high school behaviour is having an impact: "A Taco Bell restaurant in Antioch has started closing its dining room in the afternoons after managers say it has become a magnet for high school students after class, and fights have been breaking out.“At school you get suspended or something for that, and if you’re not at school you go to the plaza and fight and get away with it,” one student said.". That even includes death threats. Check out the video.

Sagetex: Area under a quadratic using limits

LimAreaI've added another problem to the Sagetex: Limits page. The problem is to find the area under a quadratic using limits. The problem is easy to formulate but explaining the solution is tedious programming. You can see a screenshot of the problem above.

The fourth round of the Chess Masters Final is in the books. Anand has sole possession of first place. The scoring in the event is 3 points for a win, 1 point for a draw. With 2 rounds left and a 4 point lead this tournament is over from a practical standpoint if not a mathematical one. You can follow the games from the site, ChessBomb (on the sidebar) as well as Livestream.

Common Dreams has more on the militarization of the school system: it's even more extensive than you think. From the link: "Turns out San Diego isn't the only school district in the country to get a $700,000 Mine-Resistant Ambush-Protected Armored Vehicle and other military baubles from a federal government overloaded with shiny lethal gimcrackery from its many failed wars. At least 120 schools and colleges in 33 states, including Florida, Georgia, Kansas, Michigan, Nevada and Utah, have gotten such geegaws, according to tenacious reporting by Muckrock and others. Texas - including the town of Cut and Shoot, population 1,000 - tops the list, with at least ten districts gleefully acquiring 15 surplus military vehicles, 64 M-16 rifles, 18 M-14 rifles, 25 automatic pistols, extended magazines, 4,500 rounds of ammunition, armored plating and tactical vests.". ZeroHedge has some quotes from the Wall Street Journal talking about how the Los Angeles Unified School District has gotten "... grenade launchers, M16 rifles and even a multi-ton armored vehicle from the program. But the district is getting rid of the grenade launchers, ".One consequence of spread of weapons is some weapons have been lost, stolen, or otherwise accounted for: "Nine California law enforcement agencies are suspended from the 1033 program, according to Cal OES. The suspensions all stem from lost weapons, including one pistol, 10 M16 assault rifles and one M14 rifle.

The San Mateo Sheriff’s Office has received 78 assault rifles and a truck through the program.  More than 7,700 M16s have been distributed  in California since 2006. In just the last two years, California agencies have also received 41 mine-resistant vehicles."

Next, with all the pressure to get technology into the school system, it's interesting to see the New York Times running an article ("Steve Jobs was a Low-Tech Parent") about how Steve Jobs and various tech CEOs having strict rules regarding the usage of technology in their own family: "...I’ve met a number of technology chief executives and venture capitalists who say similar things: they strictly limit their children’s screen time, often banning all gadgets on school nights, and allocating ascetic time limits on weekends."

Finally, the Daily Caller takes Bill Gates to task on pushing the Common Core onto YOUR kids, but not his. Given the increasingly political nature of Common Core, I think you're going to hear about this in the future.



Tikz-euclide: marking angles

MarkAnglesJust a few points of interest: I've added a little more information to the Points, lines, line segments, rays, and labels page. It explains the very basics of marking angles using the tikz-euclide.

Next, in a recent post I mentioned there has been a militarization of schools in Texas. Now there are reports that the same thing is happening in San Diego. NBC news San Diego reports that "A heavily armored vehicle is now a part of the San Diego Unified School District Police Department’s arsenal, though administrators say it will only be used for rescues.". And an article from the Daily Beast asks, "Why Does My Kids' Elementary School Need a Tank?". However you answer that question, the key piece from the article is:

"San Diego Unified School District is the second largest in California: in terms of geography, it’s about 22 miles long and 23 miles across. According to the FBI, the average school shooting lasts for 12 minutes, which is probably not enough time to get a crew assembled at the facility where the MRAP is stored, much less drive through miles of SoCal traffic. SDPD and Fire Rescue would probably be on the scene long before anyone remembered where they had left the keys to the MRAP. Even if the shooting were an atypically protracted event, or the MRAP just happened to be in the neighborhood, in the case of many campuses, the vehicle couldn’t get very close to the classrooms. In short, the critics argued, the chances that this machine could ever be useful were minimal."

Finally, there's a website: You're Getting Old! which could be useful in your class, especially if you work with rates/ratios/unit analysis. Just input a date and you'll page of information. Some statistics, such as shown below

GettingOldbut also key events in history and  milestones in that person's life.

Tikz: Template for Plotting

PlotTemplateIt started with an answer to a post at Tex StackExchange; user cyanide-based food had an "easy-to-cutomize  template with PSTricks". The output looked great and the code worked when I copied/pasted it into Gummi so I upvoted the answer and made a copy of his/her template. The problems came later for me when I had a lot of trouble using the template. After modifying the code it wouldn't even and trying to figure out what I had broken in the code was anything but easy.

Ultimately I gave up on the template but it prompted me to put my own template together using Tikz. The output is shown above and the tex file is posted on the Handouts page. I think the output looks as good as cyanide-based food's answer.  With respect to the tex file, I've added comments to make it easier to understand and customize. Here's a screenshot of the template where I've removed the graph paper background and the legend.

PlotTexmplateBIf you click on the picture you'll get a better view. Above the code had "grid=both". Changing that to "grid=none" (circled in red) and commenting out the 3 addlegendentry lines gives us a different look. The final point to mention is the plotting detail. Look closer at the picture and you might notice that the graph of sqrt(x) isn't nicely plotted near 0. That can be fixed by changing the line

\tikzset{g Line Style/.style={smooth,thick, samples=400}} to something like

\tikzset{g Line Style/.style={smooth,thick, samples=800}}

Increasing the sample size will put more "dots" on the screen so that the sqrt(x) plot looks better. EDIT: Note the color names that have been used. The option dvipsnames sets the color names that can be used. You can get a list of these different color names by looking at the xcolor documentation at CTAN.

Sinquefield Cup 2014: Fabilous!

A quick post to wrap-up the Sinquefield Cup 2014 and mention some other current events. FIRST:

The 2014 Sinquefield Cup has ended and there are 2 words that come mind to describe it: historic and fabulous fabilous. I'll go with Fabilous as the most appropriate. The organizers did a fabilous job in putting the tournament together and making it run smoothly. The players did a fabilous job in playing, for the most part, fighting chess. In a world where a free software program beats the best humans, who wants to see players agree to an early draw like happened in Topalov-Carlsen? Both players would struggle not to lose if it were Stockfish on the other side; why are they packing it in so quickly? For the most part, real fans who paid money to see the event in person got a fabilous treat. The star of the show, Fabiano Caruana was Fabilous himself. His historic performance in one of the strongest tournaments in chess history was the story of the event: 8 wins and 3 draws against some of the best players on the planet.

There's one glaring dilemma for the organizers: "How do you top this for next year?"

I've already mentioned that the "strongest chess tournament" is based on the inflated rating average so "highest rated chess tournament" is more accurate. Comparing the tournament to Las Palmas 1996 I found it a stretch to say the 2014 Sinquefield Cup is the strongest tournament. Ivanchuk's obvious decline in playing strength between then and now while his rating is basically the same makes me think the inflation is, in round terms, around 100 points. Indeed, Kasparov even tweeted: "Not great chess but more great fights!".

SECOND: Chances are you've had issues with a student using an electronic device or phone in your class. This girl used a phone in class, which was against the rules, was sent into the hallway where she was told by the assistant principal to hand over the phone. The student refused because she was "scared" and walks down the stairs to "get away" from the assistant principal only to find that the police had been called. She of course refused to give her phone to them because she was "talking to her mom" which led to 3 police officers pinning the 70 pound student to ground. You can see the news report, with video footage of the police here. On one hand you've got a student who doesn't follow the instructions of school administration and the police, but does it really have to come to what you see in the video? Can't they student be kept for detention after school? Or suspend her from school for x days for disobedience? Or call the parents and have them tell her to hand over the phone? That student attitude of doing whatever they want and not obeying the adults in charge is so typical of this generation, but does it have to end like this case?

THIRD: Remember the militarization of the police as shown in Ferguson? Military harware has come to some Texas schools. From the link: "“In all, the departments received 64 M16 rifles, 18 M14 rifles, 25 automatic pistols, and magazines capable of holding 4,500 rounds of ammunition as well armored plating, tactical vests, and 15 surplus military vehicles,” reports KHOU.".

FOURTH: The River Valley TV: LaTeX link has been updated after the URL changed. WebEquation has been down as well but I can't find it. Hopefully it will come back online soon, otherwise the link will need to be removed.

FIFTH: Infowars yet again--the videos speak for themselves. This time with a teacher taking "about a minute" to solve 9+6=15. Rather than learn to memorize addition tables and/or use the algorithm to add, it's all about changing the problem so that it's 10+ something because that addition is easier for students. GROAN. And what happens if they can't do 10 + 5? After years of lowering the bar it's really come to this.

Sinquefield Cup 2014 and more

FIRST: In the last post I mentioned that the Sinquefield Cup was almost over. He just had to avoid playing not to lose. He played to win and now it is over. Not mathematically; but assuming there's no thermonuclear war or other tragedy to keep the tournament from finishing there's no way he doesn't win. Two rounds ago and only Topalov and Carlsen had a chance to catch him. With Caruana's defeat of Topalov in round 6 it's up to Carlsen. The standings have Caruana: 7 points, Carlsen: 4 points, and Topalov: 3 points with just 3 rounds to go. Look for Caruana's streak to end tomorrow. He plays Carlsen tomorrow and if Carlsen wins or gets a draw the streak is over. If Caruana gets an advantage then I'd expect Carlsen to offer a draw and Caruana to take it. Carlsen can't realistically win the tournament so he'll want to avoid losing 1/2 a point so he can get second place. That half point would clinch undisputed 1st place for Caruana and $100,000. Why risk playing on against the World Champion and risk missing something?

After some more strange chess today you really have to question just how much rating inflation is out there. I thought the Round 2 game of Aronian-Topalov was questionable enough with Aronian missing 14....Bxd4 and then Topalov losing the resulting position which included a dreadful decision to castle queenside. Today had two more woeful games. First is Vachier-Lagrave -Caruana.LVMFCNote that it's move 16 and white has about 11 minutes left. White took a quiet Queen's Gambit, played some strange moves that had Seirawan mystified and gave black the advantage. White's about to march his king up to c3 soon (!) I can't remember any of the world's best players from previous generations (when the ratings were lower) mishandling a position like that. Or how about Carlsen -Nakamura? After Nakamura's collapse at Zurich, you had to wonder whether "Fischer-fear" would set in when playing Carlsen. Today's game makes me think it's true. Nakamura misplayed the opening and was busted by move 15. And in the previous round (round 6) Nakamura's play had Kasparov tweeting: "Did Nakamura really play Q from e1 to a5 & back to e1? Too subtle for this old retiree!". There's been enough play [EDIT] which is inconsistent with legitimate 2800 ratings.

So although this may be the highest average rating of any chess tournament ever, I wouldn't dare to call it the strongest tournament ever. There have been lots of really strong tournaments in history. Let's compare it with Las Palmas 1996 because:

  • It also had 6 players and was a double round robin tournament
  • It was recent enough that some of the players are still alive and playing.

As the link indicates, Las Palmas 1996 had Kasparov, Karpov, Anand, Kramnik, Topalov, and Ivanchuk. These were the 6 best players in the world with an average rating, according to the link, of 2756. Well off the 2014 Sinquefield Cup average of 2802 but consider some points. Ivanchuk was in his prime with a rating at 2730. Now he is nowhere near as dangerous a player with erratic play that frustrated him so much he announced his retirement. You wouldn't know it by his rating which is about the same. But more importantly let's focus on each of the players and their world championship play. It's complicated by the fact that the chess title hasn't always been unified. Consider the stats here at Wikipedia. Which tournament looks stronger?

strongestOf course you could argue that we need more time to see how well the current group turns out but clearly they have a lot of catching up to match the talent at Las Palmas 1996:

Besides this tournament there are some other notable tournaments: Linares 1993, AVRO 1938, Zurich 1953. Comparison with Sinquefield 2014 is more difficult, though.

SECOND: I've added two diagrams to the Graphics page to show the possibilities from rolling two dice.

Dice1The second diagram just has the sum of the roll; eg, (2,1) replaced by 3.

THIRD: Here's an update on how Common Core is going in each of the 50 states.

FOURTH: Education Next has a report that the new teacher evaluations are similar to the old ones. Why? It looks like the reform is being watered down: "After collecting and synthesizing data from 17 states and the District of Columbia, we found that, despite state policy changes, many districts still don’t factor student growth into teacher evaluation ratings in a meaningful way. And, despite concerns that one-size-fits-all teacher evaluation models would limit local autonomy, districts continue to have wide discretion even under “statewide” evaluation systems—and that’s not entirely a good thing. The result is that in many places there is still no clear connection between student academic achievement and educator evaluations."

FIFTH: More teens behaving badly: A 15-year-old boy in Florida got a Snapchat of his cousin holding a stack of cash, so he and four of his friends decided to rob his cousin's house. They would have gotten away with it, too, if it weren't for his cousin's pesky dogs, and the fact that the rest of his family was home. That same link mentions a 16 year old who died after snorting what he thought was cocaine and turned out to be poison. But it's not just the US. Keep reading until you get to: "Teens in Hong Kong climbed atop a skyscraper to eat a banana and take a selfie, resulting in what some are calling the "world's scariest selfie"". There's a video as well. WOW.

Sinquefield Cup 2104: Halfway done or almost over?

NakCarThe 2014 Sinquefield Cup has finished 5 of the 10 rounds. While the players enjoy a rest day today, some pundits are asking if the tournament is already over. That's because Fabiano Caruana has started with a perfect 5-0 score to take a commanding 2.5 point lead. He's shown outstanding opening preparation especially in his game against Maxime Vachier-Lagrave, and cool defense against the World Champion Magnus Carlsen. Most recently he outplayed Hikaru Nakamura with the black pieces to enter the books with one of the most impressive starts in chess history. About the only sign of weakness was in the position shown above where Caruana played 44...fxg4. Computers had, of course, found the winning shot (take a moment to find it. Answer is at the bottom of the post). The move 44...fxg4 gave white some play that kept them fighting for another hour.

Caruana's blistering start (a 3601 performance rating) combined with Carlsen's spotty play are apparent when you check the Live Chess ratings:

CaruanaThe separation between Carlsen and Caruana has dopped by a massive 30 points.

So is the tournament over? No, but it's almost over. Caruana's closest two competitors are Topalov and Carlsen at 2.5 points. If Caruana scores a mere 2.5 out of the remaining 5 games then his competitors need 5/5 to tie for first: very unlikely but not, as we've seen, impossible. If you imagine Topalov or Carlsen getting an impressive 4 out of the remaining 5 then Caruana wins with just 2 more points. The potential danger is if Caruana tries play not to lose. That sort of safety first mindset combined with a mistake here or a hard fought loss there can keep the outcome in doubt. It's Caruana's tournament to lose and decent play will bring him a victory in what has been labelled the "strongest tournament ever".

Changing gears, the "strongest tournament ever" is based off of an average rating of 2802; the highest average ever. It's certainly an extremely strong tournament but let's understand that the rating system is inflated. Just as $1 today isn't worth what it was 10 years ago, it's the same with chess rating points. Jeff Sonas wrote an article on Chessbase back in 2009 explaining a lot of the details. It's obvious now as well when you see players such as Anand who are past their prime but that's not reflected in their rating. Once again checking the latest Live Chess Ratings, I'll focus on this group of older players:

Older1It's often said that chess is a young man's game because players reach their peak in their mid to late twenties. A lot of the older players were, at some point, in the top 5 in the world. But as their play declines it doesn't  show up in their rating. Look at Gelfand. He's 46 years old, well beyond his peak, but he's still 16th in the world. Click on the ratings icon  and you'll see this:

Gelfand His rating shows an upward trend even as his chess ability has gone down. It says something about the strength of chess players today that, not so long ago, both Gelfand and Anand were battling for the world chess championship. Or how about Ivanchuk who made it to number two in the world way back in 1991 and yet today, with his erratic performances, is now at 19, down from 17. Or how about Michael Adams? His peak performance was back around 2002. And with a peak rating of 2761 (achieved recently of course) you might think that he was as good as Karpov (peak rating of 2780 back in 1994 when the ratings weren't as inflated). Let's be clear: Adams is a gifted player but Karpov is a legend. Now look at Adams' rating history:

Adams Michael Adams' recent ratings indicate he's as good as ever. Older, declining players don't show a decline when you look at their ratings; their peak rating occurs after their prime and they are still some of the highest rated player in the world. We also need to bear in mind that the nature of the game has changed. Nowadays players are getting computers to do a lot of their work. With computer preparation, players are starting the game with a position where the "heavy lifting" has been done.

As Nigel Short said in 2009,"The recent ChessBase article on rating inflation by Jeff Sonas would suggest that my rating in the late 1980s would be approximately equivalent to 2750 in today's much debauched currency". So when you hear this is the "strongest tournament ever" just remember it's more accurately described as the "highest rated tournament ever" because inflated chess ratings paint a deceptive picture of chess strength.

Black wins with 44....Bh4! (threatening R8c2). If 45. Bxh4 then R8c3 will end up winning the white queen.