# programs

## 프로그램

An app to explore numeral systems in different basis using coins.

Graphs (or networks) are geometric objects consisting of vertices and edges. We can build infinitely many graphs, but we can classify them in families depending on their properties, using what we call “invariants”. Discover how mathematicians classify graphs with this interactive app!

Play as a human or as an artificial intelligence to find out how human thinking differs from how an AI processes things. In which way does the human way of playing differ from the AI’s way of playing? What is the difference between ‘knowing’...

It’s your first day in your new job. Together we will attempt to lower the crime rate of your city. Click through the story and let us dive into a topic full of questions: Where are the limits to using artificial intelligence? How important are transparency and data safety for you? What...

An AI that uses Reinforcement Learning learns through trial and error by directly interacting with its environment. It’s similar to how humans and animals learn.

An exhibit to visualize and playfully discover the mechanisms of neural networks.

Use your finger to write a number between 0 and 9 in the left box. On the right you can see as which number the AI recognizes your input.

We sit in a self-driving car, controlled by an AI. All of a sudden, something unexpected happens. How is the AI going to react? Use the buttons to choose a scenario and see what happens.

An automatic speech recognition exhibit.
Push the “Record”-button and speak into the microphone. You can speak in German or English by selecting the corresponding language before recording.

A treasure chest lies at the deepest point of the seabed. You have a limited number of tries to find it. Special probes will help you. They tell you how steep and deep the seabed is at the current position.

Let’s play a simple game. Flip the cards to reveal numbers. You have 10 turns to reach the highest possible sum (from your 10 possible flips). On each turn you can either flip a new card, or choose one of the ones you had seen on a previous flip.

Have fun pretending you’re a piano virtuoso with the help of AI. Use the 1-8 numbered keys in your keyboard or touch the colored buttons to play a full 88 key piano. The more you pretend to be a real player, the better the AI will make you...

Move through the “Space of Pentatonic Scales” and create your own impressionistic style music by playing pieces by classical composers with only five notes.

Sound and its perception has a rich mathematical structure that allows us to understand and create sounds by mixing waves. The Spectrum of Sound is an exhibit composed of two parts: a synthesizer and an analyzer. This is the Analyzer part.

Hear sequences of numbers as if they were melodies!

Play a few notes on the piano or develop a rhythm on the drums. Try out how the Artificial Intelligence (AI) responds to your music. You can also experiment with different styles and speeds.

Dive into a multitude of topics that visualize the complex interrelations of melody, harmony and mathematics. Push the “play” button in each visualization and experience the effect of parameters.

Select an animation, press the “play” button and experiment with the parameters. Try to clap along.

Turn the wheel and get the colored dots moving. Listen carefully.

Insert new nodes and connect them. Change the corresponding sound by clicking on the node and select a new note from the scale. Define the note’s duration and apply the different embellishments. You can hear the results in real time.

Take the role of a conductor. Move your hand over the sensor on the desk and play with the volume and speed of the piece you hear. Move the slider to get support from our Artificial Intelligence (AI) musician.

Explore how we can represent the notes in a logical and useful way! The Tonnetz is a pictorial representation of the notes in the plane that reveal affinities and structures between notes and on concrete music pieces.

Which sounds can be called “notes”, and used to create music? This exhibit is an experimental platform to explore the characteristics of sound and scales.

Sound and its perception has a rich mathematical structure that allows us to understand and create sounds by mixing waves. The Spectrum of Sound is an exhibit composed of two parts: a synthesizer and an analyzer. This is the Synthesizer part.

Pink trombone is a model of the human vocal tract that synthesizes human voice from scratch, controllable with your fingers.

Snapshots are short texts on aspects of modern mathematics written by researchers visiting the Mathematisches Forschungsinstitut Oberwolfach. With this Snapshot station, you can browse through all available snapshots by sliding horizontally and read the full snapshot by sliding vertically. Each...

Math to Touch is a collection of 16 small apps, each of them opening a little mathematical world to be explored.

Explore the science of cartography and the geometry of map projections.

MatchTheNet is a game about 3-dimensional polytopes for a single player. You will meet the five Platonic Solids and their best friends!

더글라스 호프스태터의 책 ‘괴델, 에셔, 바흐’에 영감을 받은 이 게임은 학제간 작업을 포르투갈어, 스페인어, 영어를 이용하여 3차원적 사고를 연습할 수 있는 게임입니다. 이 게임은 스마트폰, 태블릿, 데스크탑 컴퓨터에서 실행됩니다.

지난 한 세기 동안 고산 빙하(alpine glacier)의 크기는 계속 줄어 들고 있고, 지구온난화가 지속된다면 이는 계속될 것입니다. 수학적 모델링을 이용하면 미래의 빙하의 모습을 예측할 수 있습니다.

쓰나미(Tsunami) 혹은 지진해일은 바다에서 일어나 해안에 충돌하는 거대한 파도입니다. 많은 쓰나미들은 해저 지형이 급격하게 변하는 지진에 의해 일어납니다. 이 전시물은 쓰나미를 수학적으로 모델링하는 방법을 설명하고, 역사적이었던 쓰나미 재앙들의 시뮬레이션을 보여줍니다.

전시용으로 만들어진 IMAGINARY 영상들의 단순하고 우아한 프레젠테이션입니다.

전시용으로 만들어진 IMAGINARY 갤러리의 단순하고 우아한 프레젠테이션입니다.

Formula Morph 스테이션을 만들어 계기판을 조종해 보세요! 여러분의 임무는 다이얼과 레버를 조정하면서 어덯게 대수적 곡면들이 변화하고 합쳐지는지를 관찰하는 것입니다.

Qi는 상수평균곡률 곡면(constant mean curvature surfaces)과 제한된 윌모어 곡면(constrained Willmore surface)들을 체험하며 볼 수 있는 프로그램입니다.

격자처럼 배치된 원형 모양의 거울들이 빛을 반사시키는 모양 속에서, 예측불가능한 변화와 대칭적인 패턴을 모두 관찰해 보세요.

이 프로젝트는 우리 지구의 수학(Mathematics of Planet Earth, MPE)과 관련된 Cartography, Dynamical system, Wator, Temperature, Cellular automata 의 다섯 가지의 체험을 제공합니다.

Dune Ash는 유럽에서의 화산폭발 시뮬레이션입니다. 화산을 위치시키고 바람의 벡터장을 입력하여 화산재의 이동을 관찰해보세요.

이 체험 프로그램을 통해 수정, 형석 또는 다이아몬드 결정 속을 날아 보세요. 결정 속의 작은 우주선을 타고 터치스크린을 보며 조종하면서 결정 구조를 관찰할 수 있습니다.

프로그램 Morenaments는 평면의 17가지 대칭군 중 하나를 선택해 대칭적 패턴을 쉽게 그릴 수 있게 해 줍니다. 대칭군의 회전중심 혹은 반사축 같은 기하학적 성질과 구조를 탐구하거나, 몇 번의 획이 전체 공간을 아름다운 무늬로 채우는 것을 감상하며 창의적인 방법으로 도안을 만들어낼 수 있습니다.

프로그램 SURFER는 수식과 형태, 즉 수학과 예술의 관계를 체험할 수 있게 해 줍니다. 명료한 수식들이 공간의 곡면으로 나타나는 아름다운 이미지들을 만들어 냅니다.

이 프로그램은 독일 수학의 해 IMAGINARY 전시에 사용되었던 프로그램 SURFER2008의 Java 기반 확장입니다.