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One million first digits of π: https://www.piday.org/million/

Find a date in π (like a time date; not talking about πnder): http://www.mypiday.com/

Find your name in π: https://www.atractor.pt/cgi-bin/PI/pib27Search_vn.cgi

More fun with π: https://lab.open.wolframcloud.com/objects/user-a596dba9-5782-467e-ae66-047a9a819454/FunWithPi.nb#sidebar=compute

Eat some π (any bakery near you)

When mathematicians get hungry…

Today*, obviously right after I had finished my home-cooked lunch, my labmates and I discovered some free leftover pizza in the kitchen area. While it’s a given that most people love pizza, it is even truer that academics love pizza. And mathematicians, a special breed of academics, are no exception. Their love for pizza is so pronounced that they named a mathematical theorem after it: the pizza theorem.

The pizza theorem states that if you cut a disk in a number of pieces that is divisible by for and greater than or equal to 8, you get two areas of equal size by alternating the slices of the disk. In other words: the sum of the areas of the odd-numbered sectors equals the sum of the areas of the even-numbered sectors.

If you cut a pizza like this, I will get very mad.

What it means is this: if you slice a pizza into a certain number of slices, and that number is 8, 12, 16 or 20 (other multiples of 4 are also possible, but let’s be honest, that gets pretty difficult to cut a pizza into more than 20 pieces), two people will end up eating exactly the same amount of pizza by eating alternating slices. The slicing does not have to go exactly through the center of the pizza (that’s kind of hard to do precisely), as long as all cuts go through the same point.

Here it is in shouty colors. Colors always make everything so much clearer.

The pizza-inspired math does not end there. Apparently, you can prove that if a pizza is divided unevenly, the diner who gets the most pizza actually gets the least crust – a 6-year-old’s dream!

Here’s another: a pizza sliced according to the pizza theorem can be shared equally among n/4 people (with n the number of slices). So 8 pieces can be shared equally among 2 people. 12 slices can be shared between either 2 or 3 people. 16 slices between 4 people, and 20 between 5. Good to remember for those pizza parties!

Pizza=Math!

Okay, I’ll leave you with some pizza facts:

  • An approximate total area of 100 acres of pizza is eaten in the US every year. That’s about 120 football fields (the standard method of size measurements). That means that if the whole of the US was covered in pizza, it would take 2.43 million years to eat it all, considering the eating rate remained constant.
  • Depending on how you define a “pizza”, the origin of pizza might not be Italian! Ancient Greeks and Egyptians were flatbreads topped with olive oil and spices. So kind of like pizza? (Nah, not really.)
  • Another math-pizza-merger is called the lazy caterer’s sequence, a sequence that counts the maximum pieces of pizza you can obtain by a given number of straight slices.
  • In 2001, which was mostly a Pizza Hut publication stunt, the first pizza was delivered to outer space. Cosmonaut Yuri Usachov was the lucky recipient.
  • The first computer-ordered pizza was delivered in 1974. Not through the internet though; the Artifical Language Laboratory at Michigan State was testing out its “speaking computer”.
  • If you thought the fancy pizza dough spinning and throwing was just a tourist attraction, you’re not entirely right. It’s actually the best way to create a uniform disk of  dough.

Obviously, I had a slice of free pizza. You might have heard of a dessert stomach, but I also have a pizza stomach. (There was also free cake later in the day, to satisfy that dessert stomach).

_____________________________________

* “Today” as in when I wrote the first draft.

Pizza facts from:

http://mentalfloss.com/article/69737/46-mouthwatering-facts-about-pizza and https://denirospizza.com/blog-post/facts-you-didnt-know-about-pizza/

A matter of kilos

It’s been the topic of a weighted discussion for quite some time, but today it has been decided: “Le Grand K” will no longer be used to define a kilogram.

“Le Grand K” is not a big box of Special K, but a platinum-iridium cylinder stored by the International Bureau of Weights and Measures in an underground vault in Paris that has defined a kilogram of mass since 1889. There are a few official copies, and many more copies, so each country has their own kilogram to calibrate to.

Last Friday (November 16th) the kilogram has been redefined so it no longer depends on a material object. Because a material object can be scratched, chipped or destroyed. Or stolen. Or accidentally thrown into the bin. And it can degrade – in fact, “Le Grand K” weighs about  50 µg lighter than its six official copies. You don’t really want to gold – ahem, I mean platinum-iridium – standard for weight to change in weight, right?

So now the kilogram will be defined based on a universal, unchangeable constant. Much better, I think you would agree. The constant of choice here is the Plank’s constant, a number that converts the macroscopic wavelength of light to the energy of individual constants of light. Representatives from 58 countries universally agreed on this new definition, so from next year, the kilogram will be constant forever.

The ampere (electrical current), the kelvin (temperature) and the mole (amount of chemical substance) have also been redefined. That means that all seven units in the International System of Units (S.I.) will be defined by universal constants:

meter unit of length
  • Originally defined as a 10-millionth of the distance between the North Pole and the Equator along the meridian through Paris, later as the distance between two scratches on a bar of platinum-iridium metal
  • Since 1983 defined as the distance traveled by a light beam in vacuum in 1/299,792,458th of a second, with 299,792,458 m/s being the universally constant speed of light.
kilogram unit of mass
  • Initially defined in terms of one liter of water, but since as a small ~47 cm3 cylinder stored in a basement in Paris.
  • Now redefined in terms of the Plank constant h = 6.62607015×10−34 J*s (J = kg*m2*s−2)
second unit of time
  • Originally defined as 1/86,400th of a day
  • Since 1967 it has been defined as the time it takes an atom of cesium-133 to vibrate 9,192,631,770 times
ampere unit of electrical current
  • Originally defined as a tenth of the electromagnetic current flowing through a 1 cm arc of a circle with a 1 cm radius creating a field of one oersted in the center
  • Now redefined in terms of the fixed numerical value of the elementary charge e (1.6602176634×10−19 C with C = A*s and second defined as above)
kelvin unit of temperature
  • The centigrade scale was originally defined by assigning the freezing and boiling point of water as 0 °C and 100 °C respectively. Note: absolute zero is the lowest temperature (0K =  -273.16 °C)
  • Now redefined in terms of the Boltzmann constant k = 1.380649×10−23 J⋅K−1
mole unit to describe the amount of substance
  • Since 1967 defined as the amount of substance which has as many elementary particles as there are atoms in 0.012 kg of carbon-12.
  • Now one mole substance contains exactly 6.02214076 × 10^23 particles. This constant is known as Avogadro’s number*
candela unit to describe the intensity of light
  • Originally taken as the luminous intensity of a whale blubber candle in the late 19th century.
  • Since 1979 the light intensity of a monochromatic source that emits radiation with a frequency 5.4 x 1014 hertz and has a radiant intensity of 1/683 watt per steradian in a given direction **
So that was “this week in science.” I’ll leave y’all with a related joke:

kilogram

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Sources/Further reading:

The international system of units: en.wikipedia.org/wiki/International_System_of_Units

The new kilogram was in the news: www.nytimes.com/2018/11/16/science/kilogram-physics-measurement.html and www.theregister.co.uk/2018/11/17/amp_kelvin_kilogram/

Comic from xkcd.com

_____________________________________________

* Avocado’s number, however, states that 6.02214076 × 10^23 guacas make up one guacamole. (I knooooow, I already made this joke).

** I have to be honest and say that I have no idea what this all means

Oh, when the ants come marching in

(No, that’s not a typo, I did not forget the “s” and the “i,” this post will be about ants)

Occasionally I go swimming. The problem is that I always lose count of how many laps I’ve done. It takes slightly too long to just remember what number the previous lap is – because my mind starts wandering. So I came up with a strategy: singing counting songs. Like “the ants go marching.”

You know:

The ants go marching one by one, hurrah, hurrah
The ants go marching one by one, hurrah, hurrah
The ants go marching one by one,
The last one stops to have some fun*
And they all go marching down to the ground
To get out of the rain…

ant GIF
This ant just stopped to have some fun.

One verse takes me about the same time to swim a lap, so it’s perfect. And because of the combination of the number and the rhyme, I don’t really forget what number I was on.

The song goes on with increasing numbers:

The ants go marching two by two, hurrah, hurrah
The last one stops to go to the loo…

The ants go marching three by three, hurrah, hurrah
The last one stops to have a wee…

The ants go marching four by four, hurrah, hurrah
The last one stops to slam the door…

etc.

However, a few weeks ago when I was happily swimming and internally singing, my mind started wandering anyway. I was wondering about the math of the song. How many ants would we need to have to make it work? And apparently, thinking about math and swimming also makes me lose count of laps.

Obviously, I did not find the answer during my swim session. But I have now. Here is the problem:

  • There is a row of ants marching down to the ground. Initially, the ants are marching in single file, then double, then three by three etc. until – let’s say – ten by ten.
  • There is always a random lonely single ant at the end of the parade who gets distracted by something, stops, and basically gets lost to the colony.
  • I want to figure out how many ants do you start with to make this song work.

The answer lies in the lowest common multiple (LCM). That’s a name given to the lowest number that is the multiple of two or more numbers. For example, the LCM of 4 and 6 is 12. Add 7 to the list and the LCM is 84. In other words, it is the lowest number you can find that can be divided by all your given numbers.

In the case of ants marching, at the end of the song, we’ll have lost as many ants as verses we’ve song. So if we sing it 10 times, there will have been 10 ants stopping to do some random action (that poor ant in verse seven though, she went to heaven), which is a lucky break because we are already looking for a number that needs to be divisible by 10 (and that number minus 10, can still be divided by 1). In other words: the answer to this conundrum lies in finding the LCM of all the numbers 1 through 10.**

Even more luck for me: there are several websites that calculate this for you (though there are some tricks to help you solve it). It turns out that the LCM of numbers 1 through 10 is 2520. In other words: there need to be 2520 ants in our initial parade to make my version of the song work. (If anyone feels the sudden urge to write a simulation to illustrates this song, please let me know; I know it could look cool.)

In case you are curious, going up to 11 requires 27720 ants, same for 12 verses, and for 20 verses we’d need to start out with a whopping 232792560 ants. The rule is that to end up with ants marching by n, you need the LCM(1,….,n).

However, considering that in the case of black garden ants, the average colony size is 4000-7000, marching up to 10 by 10 is pretty much the limit.

The most practical application of LCMs has nothing to do with ants, which are usually considered a pest even though all they really want is to clean up that crummy mess you left. No, the application has to do with solving fractions or word problems involving fractions. For example, if you share a cake with some friends, say I eat a quarter, my friend V isn’t very hungry so she eats a sixth, and my other friend S didn’t finish his dinner so is super hungry and he eats a third, you could use the LCM to figure out the denominator and calculate how much of the cake is left:

We ate 1/4 + 1/6 + 1/3
Using the LCM of 4, 6 and 3 this is 3/12 + 2/12 + 4/12
In other words, we ate: 9/12 or 3/4
So there is still 1/4 cake left.

Not for long though, I’ll probably eat it later.

Image result for that's how you get ants
Clean up after yourself when eating cake. 

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* I know I have the lyrics wrong here and it’s the little one that stops to tie its shoe but that doesn’t help with the math that I will get into later. Also, lyrics vary: while I sing have some fun, the internet tells me it’s “sucks his thumb”. Later on in the song, I definitely get more creative with the rhymes. Well, I say that got creative, but it was more likely a joint effort of a nation of six-year-olds.

** I really need to thank my friends (V&S) because I utterly confused myself by trying to find a “rule” and they basically solved my problem for me. #NerdFriends

 

 

An ignobel cause

Disclaimer: if you’re a bit hungry and/or know that reading about spaghetti will make you hungry, I suggest you go eat some spaghetti before you continue reading… But if you do, keep at least a few strands uncooked, you might need it later on.

An odd article popped up on my go-to news site the other day. And then the day after that, an article on the same topic popped up in the newspaper I was reading. It was an article reporting on the science of breaking an uncooked spaghetti.

No, I’m not joking.

And apparently, the research solves a decade-old problem. I never knew spaghetti could pose a decade-old problem, except for maybe the secret spaghetti-sauce recipe of an Italian-American family but that’s a century-old problem, I would say.

So if you’d go into your kitchen now, take a strand of uncooked spaghetti, hold it at the ends, and start bending it until it snaps, you will see what this mystery is all about. Most probably, you have now ended up with three or more bits of spaghetti. If you are super bored or think snapping spaghetti is super-fun (this is what Richard Feynman apparently thought), you can try it again. And you will notice the spaghetti almost never snaps into two pieces. Or you can just take my word for it…

In 2005, some French physicists came up with a theoretical solution to why spaghetti never breaks into two, because this unsolved mystery Richard Feynman broke his head about merited some further research…

When a very thin bar (or strand of spaghetti) is being bent, this will cause the strand to break somewhere near the middle. This first break will cause a “snap-back” effect which essentially causes a vibration to travel through the rest of the strand, causing even more points of fracture, which results in three or more pieces. In other words, is very rare to end up with exactly two pieces of spaghetti.

These French researchers were rewarded with an Ig Nobel prize for their finding. An Ig Nobel prize is a prize that is rewarded “for achievements that first make people LAUGH then make them THINK” and also the reason for my best quiz achievement ever.*

crack-control-1
Experiments (above) and simulations (below) show how dry spaghetti can be broken into two or more fragments, by twisting and bending. (Image: MIT)

And now, years later, mathematicians from MIT have added to that research by coming up with a way to ensure a dry spaghetti strand does break exactly in two: by first twisting the spaghetti before bending it. The twisting part causes stresses in the spaghetti strand that counteract the snapback effect when it eventually breaks. When the spaghetti does break in to, the energy release from a “twist wave” (where the spaghetti pieces untwist themselves) ensures there is no extra stress that would cause more fracture points. So there we go: the spaghetti breaks in exactly two pieces as long as you twist it enough.

crack-control-2
Experiments (above) and simulations (below) show how dry spaghetti can be broken into two or more fragments, by twisting and bending. (Image: MIT)

Now, this theory isn’t only limited to breaking spaghetti. Understanding stress distributions and breaking cascade also have some practical applications, according to the authors: the same principles can be applied to other thin bar-like structures, such as multifibers, nanotubes, and microtubules.

Now, if you haven’t already, go get yourself some spaghetti.

_________________________________________________________

* The question: who has one both an Ig Nobel and a Nobel prize and for what?
The whole table looked very confused and I just said very confidently “André Geim, levitating a frog and graphene” so it turns out a degree in nanotech is super useful for winning quizzes. (Actually, I’m not even sure we won and I doubt it was thanks to me answering that one question correctly, but I’m pretty sure I will never live up to that moment ever again.)

Not just your usual conference (100 years, Part VIII)

20171014_174148
Spotted in the Bell Pettigrew Museum of Natural History (St. Andrews)

Last weekend, I attended the Centenary conference commemorating the 100-year anniversary of the publication of On Growth And Form by D’Arcy Wentworth Thompson. You might have heard me mention this book and its centenary at some point?

It was not just your usual conference. While most conferences centre around a certain field or topic, this one explored the influence of D’Arcy and his book on many different fields It was the most interesting mix of people and topics at any meeting I’ve been at, it succeeded in bringing scientists, mathematicians, computer scientists, historians, artists, architects, musicians and knitters in the same room.

Also, the sessions were not organised topically, but pretty much random, which meant that even if you were just interested in a few talks (on paper), you ended up hearing the wide variety of topics that have something to do with D’Arcy. Personally, I thought this was a very clever choice of the organisers (kudos to them), and I enjoyed hearing about art, architecture, history, and yes, knitting, instead of boring ol’ science for a change.

20171015_215055.jpg

I also feel like I made some type of personal achievement. I was accepted to give a talk on the Physics of Cancer, which you might remember as the topic of my two FameLab contributions. For each of these, I had written a little song. So, in a crazy phase of over-confidence, I decided to incorporate these songs into my talk. And, why not, I also incorporated Star Wars references, weird cartoon cell drawings and pretty dodgy doodles I had drawn myself.

The response was amazing. I’ve given talks at conferences before but never have I received such positive feedback. Not only because they found the songs entertaining (I can assure you no-one fell asleep during my presentation) but I was also complimented on the clarity and accessibility of my talk (the very mixed audience, remember) and my optimistic approach to a “heavy” topic. If possible, I will from now on take this approach for every talk.

20171015_215312

Finally, I have a new favourite D’Arcy quote (it’s quite convenient to have three days full of inspirational quotes to muse about):

“(…) things are interesting only in so far as they relate to themselves to other things; only then you can put two and two together and tell stories about them.”

Closely followed by this one, actually:

“Facts are pointless unless they illustrate greater principles.”


(The comics snippets and the second quote are from the graphic novel “Transformations“.)