Joensuu mathematics students'
workshops in SciFest 2010

Updated 14.4.2010 Martti E. Pesonen

Conic sections - Kartioleikkaukset

Can you find from the inside of a circular cone a circle , an ellipse, a parabola and a hyperbola, namely all four conic section just by cutting the cone into pieces?
See and feel in our workshop the beauty of the conic sections and their applications around us all! We get acquainted with the conics for example by using mirrors and laser beams. We use traditional tools to introduce the definitions of the conic sections. Furthermore, in our workshop we see whether the conics are just theory in maths textbooks.
Contact: Sini Hiltunen [sini.hiltunen(cattail)joensuu.fi]

Polyhedra - Monitahokkaat

Did you know that also an ordinary dice is a polyhedron?
In our workshop the Platonic Solids known already in the Ancient Greece will be introduced and you will have the possibility to do such a solid for yourself. You can also use your creativity and build a polyhedron which only your imagination poses limits! Furthermore, we learn what kind of structures are found in polyhedra and clarify what kind of regularity laws they obey.
The workshop suits for all.
Contact: Kaisa Ronkanen [kaisa.ronkanen(cattail)joensuu.fi]

Probabilities - Todennäköisyyksiä

- What is probability theory?
- How do probabilities appear in everyday life?
- How can we utilize these in life?
To all these and many other questions is our workshop able to answer. Come to do, experience and simulate probabilities and very probably get an answer to the questions posed above. The topics include throwing dice, dependence and independence, samples, Monte Carlo integration, normal distribution and Monty Hall three door problem.
The workshop can be adjusted for all.
Contact: Kristian Vepsäläinen [kristian.vepsalainen(cattail)joensuu.fi]

Graphs - Verkot eli graafit

Our starting point is the famous Königsberg (Kaliningrad) bridge problem from which the graph theory was given birth. The Swiss multigenius Leonhard Euler invented a surprising simplification of the promenade problem and in this way we lead you to the fascinating world of graphs.
The mathematical structure of graphs is introduced and applied to problem solving through simple examples. You will see where graphs appear and in which even everyday life applications graphs are utilized. The topics include the Königsberg bridges, measuring, colour cubes puzzle and the graph colouring problem where we can use French stone boards (ardoise) similar to those that have been used in schools.
Contact: Esa Pulkka [esa.pulkka(cattail)joensuu.fi]

Symmetry and tilings - Symmetria ja laatoitukset

Welcome to be introduced to the wonders of symmetry and tilings. Test your own skills or compete with your partner in a symmetry game based on mirrors. Find the symmetry axis from a comlex figure. Try whether you are able to solve some tiling problems. Can you tile the plane? Furthermore you can see symmetric and non-symmetric tilings, e.g. the famous Penrose tiling.
No registration needed and the workshop suits for all.
Contact: Jussi Kotilainen [jussi.kotilainen(cattail)joensuu.fi]

Games, logic, puzzles - Pelit, päättely ja ongelmat

Quantum physic says that it is possible to drive a car through a wall - and some mathematics suffices to pass through an A4 paper sheet.
In this workshop we focus on games and problems that require logical reasoning and ability to conceptualize. Topics include Hanoi towers and 2 to 3 dimensional puzzles.
No registration needed and the workshop suits for all.
Contact: Reetta Tirranen [reetta.tirranen(cattail)joensuu.fi]

About infinities - Äärettömyyksistä

How big is infinity - what does it means in fact?
Is there only one infinity? If more, are there different sizes?
Our program concerns mathematical infinities, since of the others one knows even less!
Topics include Hilbert's HyperGrand Hotel, where infinitely many guests can check in (even if it were already full), wrapping the whole plane to a finite sphere and showing some infinite sums to be (finite) numbers.
The workshop can be modified to visitors of any age.
Contact: Toni Hämäläinen [toni.hamalainen(cattail)joensuu.fi]

Internet links and Matlab - Internet-linkit ja Matlab (Student Pilvi Puranen)

CAS Maple and Maxima - Symbolilaskentaa Maplella ja Maximalla (MSc Janne Gröhn and Olli Toivanen)

Maple is a computing software for engineers, mathematicians, and scientists. After a short overview, a comparison to an ordinary calculator is given. In addition, we will demonstrate programming with Maple by looking some interesting examples and show why a real computer is a more powerful and versatile tool than your average calculator (not to mention prettier in its output!). Finally, a few words are said about Maxima, a program much like Maple, except free and open source.

Quadrangles in plane geometry - Nelikulmiot tasogeometriassa (Doctor Jaakko Joki)

Technical & practical assistants
Mathematics major Tommi Sallinen
Doctoral students Janne Gröhn and Olli Toivanen
Doctor Heli Silvennoinen
General information: Martti E. Pesonen [Martti.Pesonen(cattail)uef.fi]

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