Stairway People

There is a stairwell in the main mathematics building on campus (MC), from the basement all the way to the 7th floor penthouse. Along that stairwell runs a number line painted on the walls, with silvery plaques marking various important mathematical constants. You can find celebrities like the golden ratio and $\pi$ , interspersed between oddities like the prime constant and $2^e$ .

Students who started 2018 and earlier will remember when the walls of that stairwell were hideous and barren. Students who joined last year only know the stairwell’s current beauty. And unfortunately, most freshmen today will have to wait until 2021 to experience the stairway constants for themselves. But when we are finally back on campus, please do your quarantine-atrophied legs a favour and visit the lonely stairwell.

Diehard readers know that I covered every number along the stairwell in a guide called Stairway Constants, which spanned issues 1-5 of mathNEWS volume 142 (W20). Still, it would be a disservice to call the series complete until we acknowledge what went on behind the scenes to make the number line happen.

The People

Prof. Kevin Hare

Prof. Kevin Hare should be a familiar name to most math students at UW, especially mathNEWS readers. He appeared in mathASKS 142.5 last winter, while serving as Interim Dean of the faculty.¹ Kevin got his BMath at UW before many of us were born. After doing his PhD on Pisot-Vijayaraghavan numbers (which appear in the stairwell), Kevin returned here to the department of Pure Mathematics. He has now been with the faculty for as long as most of us have known how to add and subtract. From 2015—2017, Kevin was also Director of the Centre of Computational Mathematics, followed by a brief gig as the Vice Dean of Engineering until the Provost’s office corrected this to Vice Dean of Mathematics. And of course, he came up with the idea and aesthetic of the number line.

Favourite stairway constant: the plastic number ( $P$ ), which happens to be the smallest Pisot-Vijayaraghavan number.

Prof. Barbara Forrest

Prof. Barbara Forrest has been a lecturer with the faculty for as long as most of us have known how to count, but she is no ordinary lecturer. For years, Barb spearheaded the development of online math instruction, which has proven remarkably useful in 2020. Many of you have encountered course materials created or delivered by her. Notable contributions include first-year calculus (MATH 137/138), and the Master of Mathematics for Teachers offered by the CEMC.

Favourite stairway constant: zero, because “much of modern human history is a result of this number.” That said, her calculus students have a fanatical devotion to tau ( $\tau$ , a.k.a. $2 \pi$ ).

Debbie Brown

Debbie Brown supported the Faculty’s various administrative and technical needs for 30 years until her retirement earlier this year. She started out typesetting documents for professors (back when that was a rare skill). Debbie then became Admin Manager in the Math Faculty Computing Facility (MFCF), where she worked for as long as many of us have known what triangles are. You can also thank her for facilitating the gradual renovation of the math buildings. Debbie has helped build the faculty’s sense of place and identity, from the Faculty Founders in MC, to the Slide Rule Display in M3, and of course the MC Stairwell Project.² Debbie’s contributions to the stairwell included coming up with the design, collecting constant suggestions from students, typesetting of the math for the plaques, coordinating the installations with Plant Operations, working with the sign and painting external contractors, and ensuring measurements for the ruler ticks were accurate.

William Tutte display (MC 5th floor)
Faculty Founders images and write ups (MC 3rd floor outside the C&D)
MC 3rd and 4th floor lighting and painting upgrades
Slide Rule Display (M3 Atrium)
Past, Present, Future (MC Comfy display case) - including a time capsule to be opened in 50 years
Items of Interest (MC 3rd floor display case near QNC bridge)
Artwork, furniture, and wall colours (MC 3rd and 4th floor elevator vestibule)
Graduate hotelling lab (MC 6th floor)
Omnitruncated Dodecaplex (M3 Atrium ceiling) - delayed due to various issues…

Favourite stairway constant: no preference.

Robyn Landers

Robyn Landers once attended UW as a BMath CS student, and to this day he still writes for mathNEWS. Perhaps you’ve read some of his articles without even knowing it. Currently, he works at the MFCF. As the UNIX Team Lead, Robyn is an admin for Linux and Solaris systems. In his spare time he is also an aspiring rock guitarist. Robyn’s contribution to the stairwell was verifying the text on the plaques and the locations of constants along the number line.

Favourite stairway constant: a three-way tie between Euler’s number ( $e$ ), the golden ratio ( $\phi$ ), and pi ( $\pi$ ).

Q&A

How did you come up with the idea for the number line?

KH: It really came about because I don’t pay enough attention when walking up the stairs. Multiple times when walking from the third or fourth floor up to the fifth floor of MC where my office is, I found myself on the sixth floor because I was lost in thought. My goal for this was to make the floor numbers so large that I couldn’t possibly miss it, and enough other visual clues that I couldn’t possibly miss it. It didn’t completely work, in that I occasionally end up on the sixth floor by accident, but not nearly as often now.

How did you come to be involved with the stairwell number line?

BF: A funny thing happened on the way to the mailroom… I went to check my (snail) mail one day and Professors Kevin Hare and David McKinnon were having a “hallway chat” (as professors often do) discussing the fact that there were not many common mathematical constants larger than $5$ . This became sort of a challenge to find constants above $5$ and so the hunt began…

DB: I was asked by the Vice Dean, Kevin Hare and the Executive Officer if I might be interested in facilitating a stairwell constant project. Naturally I was intrigued with the idea, and I have a knack for design and art in general. Kevin thought it would be cool to have a number line in the stairwell and have constants displayed between the floors to help identify where one is situated between floors. An interesting tidbit is that Debbie knew Kevin while he was a graduate student in PM. It was a pleasure working with Kevin many years later in his role as Vice Dean.

RL: Debbie Brown, recently retired from MFCF, did much of the work on this special project. She asked me occasional questions about math terminology and symbols while she was working with the company that made the plaques. Once the positions of the plaques were tentatively marked on the wall, I double-checked the accuracy and found some that needed to be repositioned.

I didn’t do the number line itself, just the verification of the locations for the pink marks for the constants. I did get the occasional look or question, and once the plaques were up, I noticed many students stopping to talk about them. It seems to be a well-liked feature.

How were the constants chosen?

(How did you decide when you had enough constants?)

KH: We asked for constants from various people. I think a call went out in mathNEWS, which actually helped give a lot of the constants. The biggest problem was finding constants greater than $4$ ; I really wanted two or three between each floor. There are lots of interesting numbers between zero and one, and between one and two, and then they get sparser.

BF: We used a number of references to help us out.

Prof. Forrest sent me the main reference used for the constants. I was pleasantly unsurprised that it was Steven R. Finch’s book Encyclopedia of Mathematics and Its Applications: Mathematical Constants, since I referred to it many times when writing Stairway Constants. In fact, this book is the only popular source for many constants in the stairwell.

DB: Naturally I contacted MathSoc and mathNEWS and asked for volunteers to send in their favourite constants. I had a great response from Math undergrads who kept the constants coming for weeks. There are SO MANY constants out there and so not all could be used obviously. I recommended a list and tried to keep roughly the same number of constants between the various floors. Some of the constants in the stairwell are not popular at all, but it makes it all interesting. No students outside of Math were involved. Many constants were rejected.

Why the north stairwell of MC, as opposed to any of the other locations on campus?

DB: The stairwell where the constants are situated was chosen because it starts in the basement and starts at zero, goes to the roof, and is the stairwell that gets the most use.

What was your favourite part about designing the number line?

KH: The fact that it made at least one of MC’s stairwells interesting.

BF: Ha ha… fonts! You would not believe how sensitive mathematicians are about fonts versus mathematical symbols. Here is a catalogue of LaTeX fonts with math support to give you an idea. I have been to many meetings where the purpose was to create a mathematical document and/or website and the meeting broke down due to the question around what font to use… every mathematician seems to have their special favourite one.

DB: My favourite part was coming up with executing the design. It was very difficult getting the number line precise between the stairwell floors. Believe it or not, not one of the measurements between the floors in MC was the same. Each floor had variances as the walls are not straight. Initially I wanted a type of non-removable tape/plastic affixed to the wall as it would provide straight lines. This did not look good at all — it looked like electrical tape and then one wondered if vandalism would occur. I ended up arranging for an external painting company to come in and hand paint the number line and ticks. This was very tedious as I had to explain to the painters how to measure out in centimetres and apply the appropriate $\flac{1}{10}$ , $\flac{1}{100}$ ticks, etc. Because the walls are not smooth, it was a challenge for the painters.

How much did the number line cost?

KH: The majority of the cost of the project was actually not for the number line. It was for upgrading the lighting in the stairwell (which needed to be done anyways) and repainting the stairwell (which needed to be done anyways). I can’t remember what the price was, but it was deemed to be reasonable.

How do installations like the number line benefit students and staff?

KH: The fact that you are asking me these questions means that the number line meant something to you, and for those people reading this article, the number line meant something to them. To me, it was something fun and something very specifically “math”.

What should we do if we find typos in the number line?

KH: Report them to me. I thought I caught all of them, but obviously not if you are asking that question. (My favourite was somebody who reported a typo in the 7th decimal place of a rather obscure constant, because they just happened to know the constant to 10 decimal places.)

Could more constants be added to the number line in the future?

(If so, which ones would you add?)

BF: We had discussed having a contest to see if students could find more common mathematical constants to add to the number line, especially constants larger than $5$ . But right now COVID has gotten in the way of many things… a challenge to undergraduates is something I would like to see soon in the future.

KH: I would like some more constants with a more computer science or statistical nature.

Are there any installations similar to the number line planned for the future?

KH: There are plans to rebuild the Omnitruncated Dodecaplex³ (or as I refer to it, the Giant Buckyball of doom). This has been delayed for numerous reasons. The way the stairwell project came about is that I had an idea and pitched it to the Dean. The same procedure was done for the Omnitruncated Dodecaplex. I suspect future projects will be decided the same way. So if you have ideas, let either myself or the Dean know.

How often do you visit the stairwell?

(Or do you prefer the elevator?)

KH: Back when I was allowed in the building, I would normally take the stairwell at least twice a day. I tended to lock my bike up by that stairwell.

RL: Every day! I never use the elevator unless I’m moving equipment on a cart. Every little bit of exercise helps when one’s job is mostly sitting in front of a computer screen all day.

Bonus: If you read What Stairway Constant Are You?, which stairway constant are you?

(Or do you identify with one not on the list?)

KH: I just went and did the quiz, and I am epsilon. As an interesting side note, I was briefly considering putting epsilon on a slider so that it could be arbitrarily close to 0. In the end I thought the fire regulations restrictions would make it more hassle that it was worth.

RL: My answers don’t point to any particular constant. Does that make me random? Imprecise? Innumerate? Pan-numerate? Superpositional? Undefined? I think plain old $6$ has some interesting properties: it’s perfect (i.e. equal to the sum of its divisors), and those divisors happen to be the first three counting numbers and also happen to be prime.