Wednesday, January 02, 2019

Today is Thirdsday! Enjoy it while you can!

Fellow Blogger James Propp has come up with a new Math holiday:


The day is Jan 3 (1-3 in America, though 3-1 in ... Everywhere else?) but only when Jan 3 is a Thursday.

It is a day where we celebrate the magic of the number 1/3.

0) For other math days to celebrate see here

1/3) James Propp's blog about Thirdsday on Monday Dec 31. Really ???   : here

2/3) Evelyn Lamb blogged about Thirdsday on Tuesday Jan 1. Really ??? : here

3/3) Ben Orlin blogged about Thirsdsday on Wedensday Jan 2. Really??? here

(Added ON Thirdsday: Matt Foreman has a video about Thirdsday: here and a blog post here)

 How come I'm the only one blogged  about Thirdsday on Thursday Jan 3 ??? (Added later- not quite true anymore, Matt Foreman also waited until Thirdsday to post on Thirdsday).
I asked Jim Propp about this. He said that he want to help prepare teachers and other eduators for the excitment of Thirdsday! If they already know the wonders of 1/3 they can prepare and lecture on it! Kudos to him! I assume that Evelyn and Ben are similar! Kudos to them! And Ben blogged ON Thirdsday so Kudos to him!

2) Darling asked me `is it a real day like Pi-Day?'  Is Pi-Day real? Is any Holiday real? All holidays are made up until they are accepted and become real. The distinction between real holidays and  made up holidays  is ... nonexistent.  One can talk of accepted and not-accepted holidays.  How long did Pi-day take to be accepted? This is prob not a well defined question.

3) James Propp's and Evelyn Lamb's  blog has many math properties of 1/3.  One educational property: I think it is the first number that students see that is an infinite decimal. My favorite unbiased use of 1/3: The Cantor Set: Uncountable subset of [0,1] that has measure 0. Really!!! My favorite biased use: its important in Muffin Math. If m>s and you want to divide and distribute m muffins to s students, there is always a way to do this with smallest piece at least 1/3. (Usually you can do better but this is sometimes the best you can do.)

4) When will the next Thirdsday come?

2019: Jan 3 is a Thursday, so YES

2020: Jan 3 is a Friday, so NO

2021: Jan 3 is a Sunday (why no Saturday? Leap year. Great- it will come sooner!)  so NO

2022: Jan 3 is a Monday, so NO

2023: Jan 3 is a Tuesday  so NO

2024: Jan 3 is a Wednesday  so NO

2025: Jan 3 is a Friday. WHAT! Why no Thirdsday?  Darn leap year! So NO.

2026: Jan 3 is a Saturday, so NO

2027: Jan 3 is a Sunday so NO

2028: Jan 3 is a Monday so NO

2029: Jan 3 is a Wedensday (Why no Tuesday? Leap year), so NO

2030: Jan 3 is a Thursday (Leap Year helped!), so YES FINALLY!

(Exercise: find a formula: if 2019 was the first Thirdsday, find the year for TD(i), the ith Thirdsday.)

So enjoy Thirdsday in 2019 when spellcheck still flags it.

In 2030 it will be an accepted holiday and spellcheck will think it's fine.


  1. For 2029, the 3rd is on Wednesday due to 2028 being a leap year. Nice post.

    1. Fixed, thanks, and of course Happy Thirdsday!

  2. Here's my contribution to Thirdsday: A long time ago, I discovered that if you fold a piece of paper in ½, then fold the top half back, then fold it ¼ of the way, then fold it back and fold it 3/8 of the way, and so on, the edge of the paper winds up 1/3 of the way from the edge! The puzzle is: How does a sequence of foldings-in-half yield the number 1/3? For a solution using continuous math, see Rapaport, William J. (1974), "Paper Folding and Convergent Sequences", Mathematics Teacher 67: 453-457,

    For a solution using discrete math (and recurrence relations), see item IV at