https://www.timeanddate.com/date/palindrome-day.html
A Palindrome Day happens when the day’s date can be read the same way backward and forwards. The dates are similar to word palindromes in that they are symmetrical.
Meanwhile, a "Palindrome Week" is defined as ten consecutive Palindrome Days:
In 2019, every day for 10 consecutive days is a palindrome in the m-dd-yy format, which is common in the United States:
- 9-10-19
- 9-11-19
- 9-12-19
- 9-13-19
- 9-14-19
- 9-15-19
- 9-16-19
- 9-17-19
- 9-18-19
- 9-19-19
It's interesting that every year since 2011 has had a Palindrome Week. It's easy to find this week -- the tens digit of the day and year must match, so this decade's Palindrome Weeks are in the teens. Also, the single digit of the month and the units digit of the year must match. This means that Palindrome Week was in January 2011, February 2012, March 2013, and onward to September 2019.
Yet somehow, I've never heard until Palindrome Week until this year. A Google search does link to an old article from 2012 about Palindrome Week:
https://www.americaninno.com/boston/happy-palindrome-day-heres-a-list-of-all-the-other-palindrome-days-in-the-next-ten-years-list/
I suspect that in 2012, people were more fascinated with either 12-12-12 (the last of a dozen dates whose month, day, and year match) or 12-21-12 (Mayan Calendar) than Palindrome Week. Likewise, the date 11-11-11 overshadowed Palindrome Week 2011. Meanwhile, towards the middle of the decade, there was more hubbub about Square Root Day (4-4-16) than Palindrome Week 2016.
Are there any other Palindrome Weeks? Well, if we follow the pattern that the tens digit of the day and month must match, then there were Palindrome Weeks from 2001-2009 -- the first nine days of January 2001, the first nine days of February 2002, the first nine days of March 2003, and so on. But these are written awkwardly -- for example, Palindrome Week 2002 started on 2-01-02. This raises the question, why are we writing the day with a leading zero (01) but not the month (2)? (The leading zero in the year 02 is logical since it comes from 2002.)
In the 2020's, there will be several Palindrome Weeks. These span the 20th-29th of the months of January 2021, February 2022, March 2023, and so on. (Of course, Palindrome Week in 2022 will be the 20th-28th, since February 2022 has only 28 days.)
In the 2030's, the Palindrome Days will be only the 30th and 31st of the month. In 2031, we will have both 1-30-31 and 1-31-31. In 2032 there is no Palindrome Day since there is no February 30th. In 2033, both 3-30-33 and 3-31-33 are Palindrome Days. In 2034 only April 30th is such a day, and so on through the decade.
In the 2040's there will be no Palindrome Week since there is no 40th of the month -- and indeed, there are no Palindrome Weeks for the rest of the century.
Notice that if we use formats other than m-dd-yy (one-digit month, two-digit day and year), then there are other types of Palindrome Days coming up. If we use mm-dd-yy, then in December 2021 we will have both 12-11-21 and 12-22-21. And using mm-d-yy, there will be another type of Palindrome Week during the first nine days of that same month. (November 2011 and October 2001 each had Palindrome Weeks of this type.)
We also have Palindrome Days using mm-dd-yy in February 2020 (five months from now). These will fall on 02-11-20 and 02-22-20. Arguably there will be Palindrome Week using mm-d-yy during the first nine days of that same month, but again, that's pushing it (since 02-1-20 isn't how anyone would write that date, with a leading zero for the month but not the day).
And finally, nearly every year that doesn't have a zero in the units or tens place will contain a Palindrome Day of the m-d-yy type. This month, that day was on September 1st (9-1-19). Of course, no one made a big deal about 9-1-19 since it's overshadowed by Palindrome Week. But I wouldn't be surprised if we start hearing about that type of Palindrome Day in the 2040's (perhaps on 2-4-42), once the m-dd-yy Palindrome Days disappear until the 22nd century.
By the way, it's somewhat annoying that Palindrome "Week" lasts for ten days. But that doesn't make our definition of Palindrome Week a bad definition (a bad name, maybe, but not a bad definition).
Under Calendar Reform, it's possible to have a week that is actually ten days -- for example, consider the Metric Week:
https://zapatopi.net/metrictime/week.html
On this calendar, September 10th-19th actually spans one week (and we can even make those dates fall on Zeroday through Nineday, as specified by the calendar). Thus on this calendar, we actually have a true Palindrome Week.
(Of course, as soon as we mention Calendar Reform then everything goes out the window. After all, the link mentions dividing the year into ten-day weeks, but not months. So who's to say that on this Calendar, this is currently the ninth month or September? And without that 9, we don't have any palindromes 9-10-19 through 9-19-19.)
Let's conclude Palindrome Week with a link to the Square One TV song about palindromes:
I was thinking about how I should have sung more Square One TV songs during my music breaks at the old charter school. Some songs (such as "Round It Off," which I mentioned last week) might have aligned with the curriculum. But others, including this "Palindrome" song, don't fit. (The Palindrome Weeks during my time at the old charter would have been in June 2016 and July 2017. June 2016 was before my first day of school, and of course July 2017 was in the summer. Perhaps if I had made it to my third year there, the Palindrome Week of August 2018 would have been in play.)
But still, I like the idea of singing extra Square One TV songs early in the school year in order to motivate the students to learn. It's also possible to start with the song first and then go back and create an activity that fits the song (that is, if there's time to do activities outside of the Illinois State text).
For example, mentioned in the song is the fact that 63 + 36 = 99, a palindrome. This naturally leads to an activity, where students reverse and add numbers to obtain palindromes. Note that some numbers, such as 89, require repeating the algorithm many times until a large palindrome is finally reached. It's also conjectured that some numbers never lead to a palindrome using this algorithm. The smallest such number is 196 (called a Lychrel number):
http://jasondoucette.com/worldrecords.html
Thus in a possible a palindrome activity, we might assign numbers like 89 to more advanced students (or if that's considered too hard, we can try smaller numbers ending in 9 such as 59 or 79). Some three-digit numbers can be assigned, but of course, no one should be assigned 196. This activity encourages students to practice multi-digit addition, whereas a traditional worksheet on multi-digit addition might turn them off.
Anyway, even if I don't give a palindrome activity, it's good for me to introduce music break to my students by singing lots of Square One TV songs, such as this one, at the start of the year.
I also stumbled upon the following Numberphile video on palindromes. Unlike the Square One TV video, here the palindromes are addends rather than the sums:
This might also be transformable into a classroom activity.
Lesson 2-5 of the U of Chicago text is called "Good Definitions." (It appears as Lesson 2-4 in the modern edition of the text.)
This is what I wrote last year about today's lesson:
Lesson 2-5 of the U of Chicago text deals with definitions -- the backbone of mathematical logic. Many problems in geometry -- both proof and otherwise -- are simplified when students know the definition.
Consider the following non-mathematical example:
Given: My friend is Canadian.
Prove: My friend comes from Canada.
The proof, of course, is obvious. The friend comes from Canada because that's the definition of Canadian -- that's what Canadian means. But many English speakers don't think about this -- if I were to say to someone, "My friend is Canadian. Prove that my friend comes from Canada," the thought process would be, "Didn't you just tell me that?" Most people would think that "My friend is Canadian" and "My friend is from Canada" as being two identical statements -- rather than two nonidentical statements that are related in that the second follows from the first from the definition of Canadian. Yet this is precisely how a mathematician thinks -- and how a student must think if he or she wants to be successful in mathematics.
And so, let's take the first definition given in this section -- that of midpoint -- and consider:
Given: M is the midpoint of
Prove: AM = MB
The proof is once again trivial -- AM = MB comes directly from the definition of midpoint.
The text proceeds with the definition of a few other terms -- equidistant, circle, and a few terms closely related to circles. Then the text emphasizes biconditional statements -- that is, statements containing the phrase "if and only if." Some mathematicians abbreviate this phrase as "iff" -- but very few textbooks actually use this abbreviation.
Notice that Dr. Franklin Mason does give the "iff" abbreviation in his text. Last year, I noticed that his Lesson 2.4 on biconditionals had an (H) symbol -- which stands for honors. It's interesting how Dr. M once considered this to be an honors-only topic. Now, he wants to emphasize the importance of definitions and biconditionals to all his students, not just his honors students.
Every definition, according to the U of Chicago text, is a biconditional statement, with one direction being called the "meaning" and the other the "sufficient" condition. Mathematicians often use the terms "necessary" and "sufficient." Many texts use the word "if" in definitions when "if and only if" would be proper -- but our U of Chicago text is careful to use "if and only if" always with definitions.
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