MathNotations

CONTEST IS OFFICIALLY OVER AND THE WINNER IS ----- NO ONE! Guess I should have offered a 64GB 3G IPad! to be awarded on Black Friday...


The floor is now open for David, Curmudgeon, and my other faithful readers to offer their own solutions.


And the next contest is...




This is a contest so students must work alone and this needs to be verified by a teacher or parent. No answer will be posted at this time. Deadline is Wed 11-17-10 at 4 PM EST.






Here's a variation on the classic motion-type problems we don't see as often in Algebra I/II but still appear on the SATs. I found this in some long-forgotten source of excellent word problems to challenge NINTH graders!

Barry walks barefoot in the snow to school in the AM and back over the same route in the PM. The trip to school first goes uphill for a distance, then on level ground for a distance and finally a distance downhill. Barry's rate on any uphill slope is 2 mi/hr, any downhill slope is 6 mi/hr and 3 mi/hr on level ground. If the round trip took 6 hours (hey, these are the old days in the 'outback'), what was the total number of miles walked?


First five correct answers with complete detailed solutions emailed to me at dmarain@gmail.com will receive a downloaded copy of my new book of Challenge Problems for the SATs and Beyond when it becomes available. Both the student and teacher(s) will receive this. (Illegal to reproduce or send electronically!). Read further...

Submission by email must include (Number these in your email and copy the validation as well).


1. Answer and complete detailed solution. If answer is correct but method is sketchy or flawed, the submission will be rejected.
2. Full name of student
3. Grade of student
4. Math course(s) currently taking
5. Math teacher's name(s) and parent's name(s)
6. Name, Complete Address of School; Principal's Name & Email address (if known)
7. Email addresses of teacher(s), parents, student
8. Phone number (in case I need to call you) - Optional
9. How your or your teacher or parent became aware of MathNotations.




VALIDATION


I certify that my student (child) did the work independently.




--------------------------------------------------------------------------------


Name of Teacher or Parent (if work done at home)



"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

"You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear. You've got to be carefully taught." --from South Pacific

Posted by Dave Marain at 12:41 PM 5 comments

Labels: algebra, contest, math contest, online math contest, rate-time-distance problems

It took a couple of weeks but the results are in -- finally!

FIRST PLACE

PINK PANDA TEAM
Canadian Academy
Kobe, Japan
---------------------------------------------------------
SECOND PLACE (TIE)

WALLINGTON HS (SENIOR TEAM)
Wallington, NJ

THE BLACK SWAN TEAM
Canadian Academy
Kobe, Japan
---------------------------------------------------
THIRD PLACE (TIE)

WALLINGTON HS (JUNIOR TEAM)
Wallington, NJ

DECATUR AREA HOMESCHOOLERS
Decatur, Il
----------------------------------------------------------
FOURTH PLACE (TIE)

LAKE STEVENS HS TEAM I
LAKE STEVENS HS TEAM II
Lake Stevens, WA
----------------------------------------------------------
Comments

• Winning score was 9 pts out of a possible 14
• Median score was 4
• Participation was down for this contest but opening it up to more than one team from a school proved very successful. Some schools which had planned on participating found the timing at the end of May to be very problematic and had to drop out after registering. I'll remember that for next year!
  
• Hardest problems involved trigonometric derivations and a probability question requiring an infinite series.
  
• This contest definitely proved harder than the first and several questions were designed for the upper level secondary student.
• Future contests may be split into a 9th-10th grade version and an 11th-12th grade version similar to AMC-10 and -12.
• Students indicated the contest was challenging but expressed interest in participating again.
  
• The open-ended questions required considerable effort on students' parts and mine in grading them!
• The winning team sent a highly detailed and original solution to one of the trig questions. They wrote it by hand and scanned it. This technology works very well for this kind of contest.
• I will probably publish 1 or 2 of the questions with answers and partial solutions on this blog in the near future.
• Any schools interested in participating in the fall should send me an email now ("dmarain at gmail dot com") to get on my mailing list. I've already received several emails. At this time I plan on keeping the contests "free to a good home"!
• I am very excited about the international flavor of these contests -- this seems highly appropriate given the culture being established by our current administration. The world really is becoming "one out of many!"
  
• As mentioned previously, one of my goals is to publish 10-12 of these contests with detailed solutions as a book or pdf document which can be downloaded for a nominal fee.
  

Posted by Dave Marain at 6:34 PM 2 comments

Labels: contest, MathNotations Contest

Important Updates:

• Several schools have requested registration up to this point so the contest will probably run on Tue Feb 3rd as planned.
• All you need to do to sign up initially is to email me! I will email you the Reg. Form and Rules/Procedures within 24 hours. Complete the form (about 5 minutes) and email it back and you're officially registered! (dmarain "at geemaill dot com")
  
• A team of students should be able to complete most of the problems in 45 minutes or less. It is not necessary to keep students for the full 90 minutes! The extra time was provided for students to enter their answers/solutions electronically.
• Scanned student solutions will be accepted if format is followed.
• Return registration form ASAP even if you have not yet identified the 6 participants. The team can have fewer than 6 members (but at least 2).
• The contest questions are copyrighted, therefore I will probably not publish all of them on this blog although I will provide some samples of questions and student responses for discussion purposes on this blog.
  
• After the contest is over, participating schools will receive results, answers, suggested solutions and certificates via email. At that time, if anyone else is interested in receiving a copy of the questions, email me.
  
• If you like the idea of this kind of contest and would be interested in signing up for the next one (probably in March), let me know via email or comments.
• I will send a template for Certificates of Participation for your school and individual participants. Top-scoring schools will receive a Certificate of Merit.
  

• WINNING TEAMS WILL BE RECOGNIZED ON MATHNOTATIONS AND WILL RECEIVE SCHOOL AND INDIVIDUAL CERTIFICATES!

• INTERESTED SPONSORS SHOULD EMAIL IMMEDIATELY (see address below) TO RECEIVE REGISTRATION FORM AND RULES/PROCEDURES!

• DEADLINE FOR REGISTRATION: TUE JAN 27th

• CONTEST WILL BE EMAILED TO SPONSORS BY JAN 30TH

• SUITABLE GRADE LEVELS: 7-12 (Some questions can be handled by Middle School students)

• 90 MIN TIME LIMIT - FLEXIBLE RANGE OF TIMES FOR ADMINISTRATION!
  TEAMS WILL BE ABLE TO PERFORM WELL EVEN IF ONLY 45 MIN ARE AVAILABLE!
  

• CONTENT: Up to and including precalculus; emphasis on Algebra II
  

• CALCULATORS ALLOWED

• FEE: NONE!

• Team event - Up to 6 participants may work together!
  
• All answers/solutions must be submitted electronically
• Some multistep and open-ended questions
• FREE! (At least this first one is!)
• Separate acknowledgments on MathNotations given to Middle and High School teams
• All students will receive a Certificate of Participation and top-scoring schools and students will receive a Certificate of Merit via email.
  

Posted by Dave Marain at 11:00 AM 4 comments

Labels: contest, MathNotations Contest

Well, it's been up there in the sidebar for 3 months and I'm sure it's been long forgotten, but we do have a winner of our contest.

Hans Rademacher was one of the most brilliant and prolific mathematicians of the 20th century. His research had broad scope from mathematical analysis to number theory including such diverse areas as analytic number theory, theory of partitions, Dedekind sums, quantum theory and mathematical genetics! Perhaps, even more significantly, Prof. Rademacher was deeply respected by his colleagues and students at the U. of Pennsylvania and known for his kindness and "charm!"

And our winner is...

SEAN HENDERSON

Here was Sean's contribution:

Posted by Dave Marain at 8:24 AM 2 comments

Labels: contest, history of mathematics, mathanagram

Poincare deserved the extra attention but it's time to move on. Our new icon holds a special place in my heart as much for his teaching and writing ability as for his original research in a field that occupied my younger days in research...

Please follow the guidelines for our contest:

DO NOT SUBMIT YOUR ANSWER AS A REPLY TO THIS POST

• Remember to email me at dmarain at geeeemail dot com
• Pls use Mystery Mathematician Oct-Nov-Dec 2008 in the subject line!
  

Posted by Dave Marain at 8:11 AM 2 comments

Labels: contest, history of mathematics, mathanagram

• Remember to email me at dmarain at geeeemail dot com
• Pls pls use Mystery Mathematician July 2008 in the subject line!
  

Posted by Dave Marain at 7:42 PM 0 comments

Labels: contest, history of mathematics

For now, we will be doing a monthly version of our International Math Idol (open to suggestions for naming the contest since I keep changing it!).

DO NOT SUBMIT YOUR ANSWER AS A REPLY TO THIS POST (read on)



Remember to email me at dmarain at gmail dot com with
(1) The name of the mathematician
(2) Some interesting info re said person
(3) Your source (links, etc.)
(4) Your full name and the name you want me to use when acknowledging your accomplishment
(5) If you're new, how you found MathNotations
(6) Your connection to mathematics

Our icon this month was multi-faceted but was best known for the opposite of that description!

Posted by Dave Marain at 6:37 AM 0 comments

Labels: contest, mystery mathematician

As the number of MathNotations feed subscribers has dramatically increased, it seems unfair to leave the Mystery Mathematician just in the sidebar. One of those who solved this week's contest suggested I post it in a separate entry -- great suggestion. Thus far we have three winners and I'm hoping others will recognize the image to the left or use their research skills to identify him. I will announce all of the winners on Wed 2-27 so you still have time. I'm tempted to give a hint, but I'll hold off..

Don't forget to email me (dmarain at gee-mail dot com) with the information - PLS DO NOT POST THE NAME IN A COMMENT!

Also, try to include some anecdote about the mathematician and your source if possible. If you wish, you might also include some personal information so that I can get a feel of who is responding to this contest.

ALSO:
THERE ARE ONLY 4 MORE DAYS LEFT IN THE MATHNOTATIONS SURVEY!
The responses may not be random nor the poll scientific, but the results are nevertheless interesting! You need to visit the site to vote in the sidebar.

Posted by Dave Marain at 2:33 PM 1 comments

Labels: contest, mystery mathematician

Do you see the big picture?
R U ready for a more contemporary mathematician? He belonged to a special group. I hope this is simple for you...
Remember to email me with your answer and include an interesting anecdote.
If you're reading this from a feed, don't forget to visit the site to see the image in the sidebar.

Posted by Dave Marain at 8:29 AM 0 comments

Labels: contest, history of mathematics, mystery mathematician

I didn't announce this week's Mystery Math Contest to see how that would play out. To be fair to those 200 or so subscribers to MathNotations who get a feed redirected through Feedburner, I guess I should mention it from now on, since the feed only shows new posts, not changes in the sidebar.

Anyway, we have two winners this week who correctly identified the one and only Fibonacci. BTW, this extraordinary gentleman had more names than George Foreman's sons! TC below mentioned one of his other names...

After visiting several websites, I found that he had devised some interesting word problems that seem to have survived to this day in one form or another. So now we know the rest of the story!

The following is from his most famous work, Liber abaci:

(1) A spider climbs so many feet up a wall each day and slips back a fixed number each night, how many days does it take him to climb the wall.
(2) A hound whose speed increases arithmetically chases a hare whose speed also increases arithmetically, how far do they travel before the hound catches the hare.
(3) Calculate the amount of money two people have after a certain amount changes hands and the proportional increase and decrease are given.


Here are our winners...

Mathmom!
Here's the info she supplied (the math symbols went a bit awry when I copied this from her email):

The mystery mathematician is Fibonacci. One interesting fact is that his real name was Leonardo Pisano.

Liber quadratorum, written in 1225, is Fibonacci's most impressive piece of work, although not the work for which he is most famous. The book's name means the "Book of Squares" and it is a number theory book which, among other things, examines methods to find Pythogorean triples. Fibonacci first notes that square numbers can be constructed as sums of odd numbers, essentially describing an inductive construction using the formula n² + (2n+1) = (n+1)². Fibonacci also proves many interesting number theory results such as: there is no x, y such that x² + y² and x² - y² are both squares, and x⁴ - y⁴ = z² has no non-trivial integral solutions.

He also defined the concept of a congruum, a number of the form ab(a + b)(a - b), if a + b is even, and 4 times this if a + b is odd. Fibonacci proved that a congruum must be divisible by 24 and he also showed that for x, c such that x² + c and x² - c are both squares, then c is a congruum. He also proved that a square cannot be a congruum. The Liber quadratorum alone ranks Fibonacci as the major contributor to number theory between Diophantus and the seventeenth century French mathematician Pierre de Fermat.

And our 2nd winner is
TC
who offered:

That's Leonardo Bigollo of Pisa.

This description of a famous sequence popularized by another famous Leonardo's code is interesting:

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?

It is almost a rite of passage for most math students to discover the closed form expression to this (featuring the Golden ratio, of course).

Posted by Dave Marain at 7:30 AM 0 comments

Labels: contest, mystery mathematician

Update: And the winner once again is...
Lynx!

Here's her contribution:

Jean le Rond d'Alembert is also famously known for incorrectly arguing in Croix ou Pile that the probability of a coin landing heads increased for every time that it came up tails. In gambling, the strategy of decreasing one's bet the more one wins and increasing one's bet the more one loses is therefore called the D'Alembert system. (WIkipedia)

From my reading of several biographies, it sonds as if he is another Cauchy - cantankerous, with many enemies and few friends.

My thoughts--
I've always associated D'Alembert with the Ratio Test for Infinite Series in Calculus but that's one of his minor accomplishments. He also solved the Wave Equation in Physics - not too shabby! On a personal note, his mom left him on the church steps when he was an infant. Later in life, when she wanted to reunite with him, he rejected her...
---------------------------------------------------------------------------------------------------------------

Did you already notice I changed the image in the sidebar? Before I give a hint, I'll leave it up for another 12 hours as is.
Don't forget to email me at dmarain 'at' 'gee' mail dot com with your answer. As always, the name is not enough. Include a fascinating fact or anecdote about this famous individual and a reference or link that you used.

Posted by Dave Marain at 8:08 AM 0 comments

Labels: contest, famous mathematicians, history of mathematics

What does that say about me that I am amused by that famous pun in the title of this post! Cauchy has always been a favorite of mine and his famous Integral Formula has blighted the youth of many young mathematicians in their Complex Analysis course! I recall one of my high school colleagues annually wearing a T-shirt with this formula imprinted on it on the day of the math finals. I don't believe it gave away any answers to her students!

Anyhow, we did have two winners in this week's contest. I intentionally did not announce this edition of the contest in a post as I wanted to see who would notice the new image in the sidebar! BTW, I certainly didn't expect my Technorati rating or Social Ranking to spike because of this and I was not disappointed!

Winners:
TC
Lynx

Here are TC's 'punny' comments:

Hi Dave,

It is not as if you had exhausted most others that you had to pick a
'residual' mathematician :-)

I first thought it might be L'Hospital.

Interesting anecdote:

Lagrange advised Cauchy's father that his son should obtain a good
grounding in languages before starting a serious study of mathematics.


Here's Lynx's comment/anecdote about Monsieur Cauchy:

The mathematician is Augustin-Louis Cauchy.

A quote by him (courtesy of www-history.mcs.st-andrews.ac.uk ): [Regarding √(-1)]: ... we can repudiate completely and which we can abandon without regret because one does not know what this pretended sign signifies nor what sense one ought to attribute to it.
Said in 1847

Also, according to Agnesi to Zeno Over 100 Vignettes from the History of Math by Sanderson Smith, he was a teacher at the Ecole Polytechnique. While Evariste Galois was trying to gain admission, Cauchy lost a paper written by the young man.

He was a staunch Catholic and, according to the Catholic Encyclopedia (http://www.newadvent.org/cathen/03457a.htm ): During the famine of 1846 in Ireland Cauchy made an appeal to the pope on behalf of the stricken people.

According to this website (http://web01.shu.edu/projects/reals/history/cauchy.html ), Cauchy delayed the publication of Niels Abel's masterpiece because Abel called him a bigoted Catholic.


Okay, that's enough. I'm done researching for now. Thanks for an evening of entertainment.

Posted by Dave Marain at 5:51 AM 6 comments

Labels: Cauchy, contest, famous mathematicians, history of mathematics

Our winners:
tc
mathmom

Mary Everest Boole was a remarkable woman. Her uncle, Colonel Sir George Everest, to whom she was very close, was the Surveyor General of India. He was largely responsible for completion of the trigonometric survey of India along the meridan arc from the south of India extending north to Nepal. The completion of the Indian survey allowed the subsequent survey of Mt. Everest (at the time un-named) and calculation of its summit height. It was later renamed in honor of George Everest.

Through her uncle, Mary met George Boole, an already famous mathematician. Mary enjoyed her time with Boole both socially and intellectually and they soon married. Even though Mary was 17 years younger than George, they were still very close companions and had a very successful marriage. During the next nine years, Mary and George had five daughters. Yet, this happiness would not last for long. Tragically, George caught pneumonia and died leaving Mary alone with her youngest child only six months old.

Mary Everest Boole was a miraculous woman who, widowed for fifty years, raised her five daughters and made countless contributions towards the mathematical education of many girls and boys. Mary considered herself a mathematical psychologist. Her goal was to try "...to understand how people, and especially children, learned mathematics and science, using the reasoning parts of their minds, their physical bodies, and their unconscious processes."

Mary was recognized in England as being an outstanding teacher. One of Mary's pupils was to write later, "I thought we were being amused not taught. But after I left I found you [Mary] had given us a power. We can think for ourselves, and find out what we want to know." Many of Mary Boole's contributions can be seen in the modern classroom today.

tc found this fascinating anecdote:
Niece of a famous George AND wife of a famous George! (Note the
Boolean operator)! A maven of mathematical pedagogy! - A particularly
apt choice for this blog!

I found the following quote particularly interesting:
"I have had homicidal impulse at the touch of other stimuli. When I
was quite young, I used to speculate on the problem why I did not try
to kill someone who worried me. It was not love of my parents that
hindered me; in those moods I was incapable of fear. It was not regard
for God; I considered that God made me as I was and could not
reasonably be angry with anything I did. It was -- I always came back
to the same conclusion -- it was that I thought that if I killed
anyone the police or the hangman or someone would stop my working for
algebra. Besides I felt that all stormy passions in themselves
interfered between me and algebra. Hate and revengefulness,as well as
love and fear, vanished, like burned paper, when they threatened to
interfere between me and algebra (34)."

- from The Forging of Passion into Power (London: C.W. Daniel Company,
1910), found online at http://www.troubling.info/boole10.html

mathmom found the perfect web site to search (sorry, I'm not sharing that at this time!) and commented:
The only woman I could think of before searching was Ada Lovelace and I didn't think the photo was her, though I'm pretty bad with faces. If I'd found a different photo of Boole, I might not have been sure it was the same woman.

I'll leave Mary's picture up there for a couple of weeks. I will probably do this contest biweekly from now on due to 'overwhelming' response!

Posted by Dave Marain at 5:58 AM 0 comments

Labels: contest, Name that Mathematician

As much as I revere Archimedes, life is a series of hellos and goodbyes (Billy Joel has a way with words). Again, if you think you know who the famous woman in the sidebar is, email me at "dmarain at g-mail dot com".

Please do not put your answer in the comments section of this post - we do not want to give it away until the contest is over! I will give up to 48 hours depending on how many emails I receive.

Don't forget to include some curious, fascinating or esoteric fact relating to her mathematical career or some compelling personal anecdote. From what I've read of her, the possibilities are many! Please cite your sources (link) for verification.

If I don't get a response within 12 hours, I will post a hint either in the sidebar or in this post.

Hopefully, this time, one cannot right-click, ctrl-click or view source to find her name!
I know those of you with advanced search skills will find her fairly quickly, but, remember, the name is not enough!

Happy Hunting!

Posted by Dave Marain at 5:44 AM 0 comments

Labels: contest, famous mathematicians, history of mathematics

Ok, the secret's out. Start ordering your
Archimedes and Eureka -- Nature Abhors a Vacuum T-Shirts.

It was a difficult decision, but the results are in (although we still haven''t heard from Palm Beach County). The top 3 submissions based on the log_b²(b⁶) entries in the first ever MathNotations: Name that Mathematician Challenge are -- in no particular order --

Mathmom
Eric Jablow
tc

I came in a distant 4th (I am going to appeal this). Of course, it was only fitting that I chose the 'Arc-Man' to lead off, since one of my personal favorite posts of all time came earlier this year:
The Genius of Archimedes: Parabolas, Tangents, ....
Anyone recall I attempted my first complicated diagram, suggesting how Archimedes proved that light emanating from the focus of a parabolic surface are reflected in parallel rays (and conversely)?

By the way, one of the better explanations for kids of his discovery of the displacement principle can be found here.

Ok, here are the details:
Mathmom found the following fascinating fact here:
Archimedes invented a puzzle called the Loculus (or the Stomachion,
the Ostomachion, the Syntemachion, or Archimedes' Box). It's like a
huge, complex, tangram. In November of 2003, Bill Cutler used a computer program to enumerate all solutions. Barring rotations and reflections, there are 536
distinct solutions.

Eric actually used something called a book (for youngsters out there, here is a link to explain the meaning of this obsolete term) to find the following information about Archimedes' perspective on pure math vs. science:

ARCHIMEDES OF SYRACUSE (c. 287-212 B.C.), son of an astronomer, was
Greece's star mathematician. By avocation he desired the pursuit of
mathematics proper, and he was wholly and passionately committed to
mathematics at its "purist." But by world reputation he was an
engineer, especially in the field of military engines, even if he
protested that he derived no satisfaction from this kind of work. And
when confronted with the problem of determining whether a golden crown
was made of pure gold or was alloyed with silver, he initiated the
method of Hydrostatics for the purpose.

Scientist-professors will always be the same. Archimedes, when
heading the Weapons Research Group for the Syracuse Department of
Defense, would write letters to friends that he was yearning to return
to the Campus and do nothing but pure research for its own sake. But
he was apparently doing classified work to his last breath, literally
so. And when he found his theorem on Hydrostatics he was so excited
that he insisted on talking about it to the man in the street.

I won't actually publish tc's joke regarding one of Archimedes' engineering feats (young children might find their way to this blog), so I will leave it up to my readers to invent their own...

Finally, I promise, from now on, not to the use the name of the mathematician in labeling the image file! Duh...

Posted by Dave Marain at 5:47 AM 4 comments

Labels: contest, Name that Mathematician

Update²: Only one submission thus far (and a good one!) so I will give our readers another day to email me some fascinating fact about 'A'! Ironically, Isabel, over at God Plays Dice, has a humorous post on attaching names to faces of current mathematicians. What are the odds! As with all experiments, we'll see how this challenge is responded to before making it a regular feature!

Update: Mathmom, reminded me that one can right-click on a PC and see the name of the image file. Working on a MAC, I forgot that. Well, this first picture might be a freebie, but you still need to wow me with some esoteric fact about him! Next time, I'll rename that file!! I also removed the personal info requirement (again, thanks to mathmom's astuteness!).

Starting today, we are introducing a different kind of challenge. Look at the image near the top of the sidebar. Here are the rules (read these carefully before submitting):

DO NOT NAME THE FAMOUS MATHEMATICIAN IN A COMMENT! (If you did already, I will delete it!).
Instead, send me an email at "dmarain at gmail dot com" with the following information:

(a) The name of the person
(b) One fascinating fact about her/him; it doesn't have to be what made that person famous -- I'm looking for the unusual or curious here, be it mathematical or something personal...
(c) Please cite your source for this fact (include the link) - I need to verify its authenticity

I will choose the top responses received within 24-48 hours of the time the picture first appears. Earlier submissions may receive higher ranking than later submissions. I will announce the winners in a couple of days and, of course, include the fascinating facts as well.

Note: I realize that students today have extraordinary online research skills (although one cannot enter an image in Google!), but, remember, the winners are not only determined by giving a name. Feel free to share this with students. They can enter too!

Posted by Dave Marain at 7:48 AM 2 comments

Labels: contest, famous mathematicians, history of mathematics