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## 1 What is Matherhythm?

Matherhythm is a show that blends mathematics, music and humor in a stand-up comedy format. The idea of writing Matherhythm originated as a reaction against a way to popularize science, so much popular nowadays, consisting of just lecturing, sometimes in a distant tone. We were dreaming of a show where the spectator would laugh -yes, even laughing his head off-, this not refraining from enjoying informative content presented in a rigorous way. We knew that starting a new endeavor is the hardest part of it. One of the main difficulties lay in how to combine mathematical and musical contents so that the final piece would be seamless, and on top of that, seasoned with the suitable dose of comedy that would nothing but enhance the delicate balance between science and humor. The humorous part of the show shouldn't wolf down the scientific part; otherwise, scientific content could become confuse and hard to follow. Also, the scientific part has to gracefully dissolve in the humorous part in a sort of respectful symbiosis. You want to make people laugh and at the same time to keep their interest in the scientific content; furthermore, laughing should kindle and maintain that interest. Therefore, in Matherhythm we put forward mathematical content - exact division, division with remainder, greatest common divisor, Euclid's algorithm and evenness principle - along with musical content - time span, pulse, rhythm formation, and timelines -, and we show how those mathematical ideas can be used as a principle for composing music. Matherhythm ends with a piece for African bells called gamamla, which belongs to the music tradition of Ghana. That piece is based upon all ideas presented throughout the show.

## 2 Inside Matherhythm

### 2.1 The mathematics

The mathematical concepts in Matherhythm are presented in ascending order of difficulty. We start off with exact division, which is also thought of as formation of groups and not merely as manipulation of numbers. In the Figure 1 we can see the slide corresponding to division as formation of groups.

Figure 1: Division as formation of groups.

From here we move on to division with remainder, which is again explained both in the classic way and as formation of groups. Then, we generalize and review the general formula of the division as well as some of its basic properties.

The greatest common divisor of two integer numbers is the next concept to be introduced. We remind our kind audience the classical way to calculate it, that is, to find the prime factorization of both numbers and take the primer factors common to both numbers with the least exponent. At this point, we proudly present Euclid's algorithm, which is based on a beautiful, simple property of division. We show how this algorithm is much more efficient and conceptually elegant than the classic method (see Figure 2).

Figure 2: Euclid's algorithm.

Finally, we illustrate Euclid's algorithm by giving some examples (Figure 3).

Figure 3: Examples of Euclid's algorithm.

2.2 The music

In the music section several music concepts come up; they are mainly related to rhythm, that is, the duration of musical events. We begin by introducing the concept of time span, a fixed amount of time whose division into equal parts gives place to pulses (Figure 4).

Figure 4: The division of the time span.

Next, the definition of rhythm appears, which is thought of as distributing notes among the pulses. The last concept to be presented is timeline. A timeline is a rhythm that is repeated throughout a piece and serves as temporary and structural reference (Figure 5).

Figure 5: Formation of a rhythm.

### 2.3 Rhythm is a killer

In the third section of the show mathematics and music, as promised, are blended. In the mathematical section we talked about division and its properties; in the musical part, the concepts were related to the division of the time span. Could there be an unexpected, deep connection between them? Yes, there is, and the connection is found in the fact that both consider division. We start by taking a 12-pulse time span. We then explore the following ideas: how to generate rhythms by using the divisors of 12; resulting rhythms obtained from this idea; how to generate rhythms when the number of notes is not a divisor of 12; presentation of the evenness principle and its importance in world music; rhythms with a prime number of notes. The illuminating and fertile idea here is the evenness principle, which answers the following question: Given k objects, how to distribute them on n boxes as evenly as possible? In our musical context that question becomes that of how to distribute k notes among n pulses as evenly as possible. For Matherhythm, the number of pulses is 12. The first idea that comes to mind is take k as the divisors of 12, and that allows us to generate a few rhythms (Figure 6).

Figure 6: Formation of a rhythm with 4 notes and 12 pulses.

Of course, the formation of the rhythm itself is related to division conceived as formation of groups. We explicitly show how to obtain the rhythms through division (Figure 7).

Figure 7 : Formation of a rhythm through division.

What happens when k does not evenly divide 12? In that case, division is generalized to the most even distribution. By applying the evenness principle we are able to obtain rhythms of 8 notes and 7 notes (Figure 8).

Figure 8: Formation of a rhythm of 7 notes and 12 pulses.

We again show the whole process of rhythm formation. This time we apply Euclid's algorithm and division as formation of groups (Figure 9).

Figure 9: Applying Euclid's algorithm and division to obtain even rhythms.

Finally, we play a musical piece with all the rhythms that we generated, those given by the divisors of 12 and those obtained from applying the evenness principle. The piece is played on a 8-bell set; the bells are African. This piece actually belongs to the Ghana music tradition and is called gamamla. In world music it is common to find pieces that make use of the evenness principle.

## 3 The humor

On this show we explored the possibilities of humor from several standpoints: puns (the scene where timelines are explained), absurd humor (the troll scene, the shadow scene), and -let's call it this way- poetic justice humor (serious moments of the presentation). Although most maths teachers -the vast majority, we would dare to say- think humor should be exiled from classrooms, we quite the contrary do think humor, if well distilled and in fair doses, provide the necessary mental hygiene to face the matter in question. Humor releases tensions, predisposes your mood to demanding work, and injects the required courage to learn. As a case in point, we comment more deeply on a couple of scenes from the show.

Serious moment of this presentation

With the series of serious-moment-of-this-presentation gags we intended to demolish the figure of the pedantic professor, so full of arrogance, with his pompous tone of voice, that all of us have got to know and heartily hated. We wanted to tear down that symbol of intellectual arrogance through poetic justice and also to raise a laugh. We came up with this idea of adding more and more ridiculous elements to the pedantic professor: first, a red, undignified, mortar board; next, the same cap plus a pair of fake glasses and a prominent nose (see Figure 10 below); finally, all the above plus a clown red foam nose.

Figure 10: Serious moment of this presentation.

In this scene we wanted to put the two speakers in a dire predicament. Once again humor is created through a change of status. The speakers' shadows rebel against them without apparent reason. The speakers, so self-assured, feel now helpless without their shadows and wonder whether it would be possible lecturing seriously without having a shadow, so afraid are they of making a fool of themselves (see Figure 11). Once more, we are in the presence of criticism of academic pomposity, intellectual arrogance, and extreme self-importance. The speakers will have to try their hardest to get them back and thus carry on with the show.

## 4 Visual aspects of the show

Matherhythm wouldn't be possible without the video illustrations projected on the screen. All concepts addressed during the show have their graphic counterpart on the screen. The art work of this video was carefully designed by Gutxi, our art director. It represented a tough challenge to structure the content of the show so that the audience could absorb it in a entertaining and simple way. Visually, the tone of the show is led according to a certain color scheme. A slightly saturated red is used to transmit mathematical impressions:

Figure 12: Red color is for the mathematics section.

An ocher yellow surrounds the unfolding of music:

Figure 13: Ocher color is for the music section.

Shades of the two colors so far used are displayed for the common section:

Figure 14: Shades of red and ocher for the common section.

and during all the show shots of blue cooling down our mind, preparing the audience for the serious moments of the presentation:

Figure 15: Cold blue for the serious moments of the presentation.

There is nothing more boring and drowsy that a talk with dull slides. We are sure our readers agree with us on this one. If on top of being visually dull, the slides are overcrowded with text from head to foot, we will have an audience full of boredom, sadness and despair. We have tried to beat all that with engaging, original graphic animations. From our art director's imagination designs were flowing to the screen. The troll animation was particular hard. Frame by frame, drawing by drawing, we were sketching how the appearance of our dense friend would be like.

Figure 16: The dense troll.

## 5 Maths Week Ireland

Maths Week Ireland is a yearly event to celebrate maths across the Isle of Ireland. In 2011 Maths Week broke all participation records: from October 15th to 22nd, an estimated 150,000 people participated in the activities. Maths Week Ireland is an all-Ireland celebration of Maths that started five years ago. Sheila Donegan and Eion Gill, from CALMAST (which stands for Centre for the Advancement of Learning of Maths), had this bright idea of bringing maths closer to people of all levels, ranging from primary schools to colleges, by all means possible, including shows in the streets. Their idea was to show that maths is not only that dry, disheartening set of rules that some passionless, narrow-minded teaching has turned it into. Maths is a celebration of thinking, a celebration in which pleasure, beauty and fantasy are all attired as splendorous as imaginable in their fancy dresses of logic, rigour and tenacity. For two consecutive years Contrastheatre had the privilege to participate in such an important event. Maths Week always starts with Maths in the Street at the top of Grafton St. from noon to 4:00pm. A bunch of brave mathematicians sells their commodity, a particular one: mathematics, fun mathematics. As hawkers crying out, they present their goods. Some offer maths and magic; others maths and music; there are also intriguing puzzles and mind-absorbing games. Here you have a short video showing our participation.

In Dublin, doing maths in the street.

The newspaper The Irish Times showed interest in our work. At the end of the performance that took place at Froebel College of Education, a journalist interviewed us. They also recorded some parts of our show and made a video, which was uploaded to its website.

Our show at Froebel College of Education (recorded and edited by The Irish Times).

Below you have the article, Rhythm revealed by numbers, they wrote out of the interview.

Figure 17: Our work for Matherhythm, reviewed by The Irish Times (November, 2011).

Sometimes we go to humble schools. It doesn't matter; what really matters is whether you move your audience. Maths Week is intended for all schools and backgrounds. Arousing interest for maths is our ultimate goal. Here you have a video shot at small school gym. Notice how much fun the girls were having.

Matherhythm at Saint Michael's School.

## 6 Performances

Matherhythm and Materritmo have been performed at the following places, among others:

• Maths Week Ireland 2011.
• CosmoCaixa, a popular science museum in Madrid. Our show took place to celebrate Maths Day in November 2011.
• Science and Technology Museum in January 2012.
• Stat Alicante, a big popular science fair that was held in May 2012.
• At the Vigo Drama School, in the context of innovative education project run by Carmen Quinteiro and Miguel Mirás, maths professors at Universidad de Vigo.
• Science on Stage (Spanish contest) 2012.
• Maths Week Ireland 2012.

### References

• Maths Rhythms. Video published by The Irish Times on October 19th, 2011.
• . Official website.
• Rhythms revealed by numbers. Article published by The Irish Times on October 19th, 2011.
• Science Gallery. Review of our show performed at the Dublin Science Gallery on October 21st, 2011.