# Discover more Mathamazing

## Exhibit descriptions

**Catenary**

Build an arch that won’t collapse. Balance building blocks on an arch-shaped template, then remove the template and test whether the building blocks stay in place or collapse. The shape formed by the building blocks is a catenary arch, typically used in architecture for strength.

*Themes: geometry, catenary, shape, arch, structures*

Curriculum links: Mathematics – geometry and topology

**Cycloid**

Which ball will ‘win the race’ to reach the end first? Race two balls down two separate tracks: one straight track (which appears to be shorter) and one curved or cycloid track (which appears to be longer).

*Themes: cycloid *

Curriculum links: Mathematics – geometry and topology

**Manacles**

Can you untangle yourselves and get free? Two people put on interlocking manacles or handcuffs. They must work out how they can untangle themselves from each other without removing the manacles from their wrists. This puzzle relies on patience, lateral thinking skills and topology.

*Themes: topology, problem solving, puzzle*

Curriculum links: Mathematics – geometry and topology, puzzles and number tricks

**Range Finder**

Measure the distance to different targets using two cameras and trigonometry instead of a tape measure.

*Themes: trigonometry, distance, measurement*

Curriculum links: Mathematics – geometry and topology

**Data Gathering**

Test your reaction time and compare to others. Enter your details about hair colour, age, even pet preference on a screen, then take the reaction timer test and see how you compare to people who are similar or different to you. Which group had the fastest and slowest reaction times and what relationships do you notice within and between groups? Are all relationships important, or are some relationships coincidental?

*Themes: data, statistical distribution, graphs, correlations, causation*

Curriculum links: Mathematics – statistics, probability and chance

**Balanced Ternary**

Can you work out the mass of an unknown object? Compare the object to a series of known masses using a novel counting system known as balanced ternary. While we are more familiar with our traditional counting system of base ten, this exhibit shows how a counting system based on threes (ternary) can be used as an alternative.

*Themes: counting systems, base ten, ternary, mass, puzzle*

Curriculum links: Mathematics – numbers, fractions and operations

**Parabola**

Will you always hit the target? Drop a ball anywhere onto a parabola-shaped dish and notice how the ball rebounds, then lands each time against a disc suspended above the dish (the focal point).

*Themes: parabola, focal point, focus, reflection*

Curriculum links: Mathematics – geometry and topology

**Chances Are**

Predict where the ball with land. Drop a ball through a series of pegs that are arranged in Pascal’s triangle formation and watch where the ball lands at the base. Check a distribution graph on the screen to see the pattern of where each ball has travelled and landed over time.

*Themes: probability, chance, Pascal’s triangle, statistics, statistical distribution, Law of Large Numbers*

Curriculum links: Mathematics – statistics, probability and chance

**Rolling Block Maze **(Mega Maths Floor Puzzle)

Can you make it through the maze? Roll a giant rectangular prism puzzle piece along the maze pathway. This will test both your spatial and problem solving skills. Great for small groups.

*Themes: puzzle*

Curriculum links: Mathematics – puzzles and number tricks

**Divergent Series**

Is this an impossible task? Stack four loose blocks on top of a fixed block, so the top block overhangs to reach a line one block length away. You could use an infinite number of blocks in an attempt to reach a line several block lengths away.

**Convergent Series**: This is a thought experiment which challenges you to cover up a square, then a rectangle, by half its area each time. Can the area ever be truly covered?

*Themes: series, sum, fractions, area, length*

Curriculum links: Mathematics – geometry and topology

**Shapes in Nature** (multimedia)

Explore the beauty of fractals on a touch screen and observe how shapes re-appear and repeat, just as they do in the structures of snowflakes and plants.

*Themes: fractals, patterns, Nature*

Curriculum links: Mathematics – geometry and topology

**Ellipse**

Will the ball always roll into the hole? Roll a ball down a small ramp and around an elliptically-shaped billiard table. If the ball rolls over the ellipse’s focal point, it will always roll into a hole at the other end of the billiard table.

*Themes: arithmetic, patterns, ellipse, focal point, reflection*

Curriculum links: Mathematics – geometry and topology

**Flip Flop and Digital Counter**

Drop a disc down through a series of flip flop gates that are stacked one above the other. The gates can either ‘flip’ or ‘flop’ to divert a falling disc either left or right. Notice how the flip flop gates are labelled ‘0’ and ‘1’ to model a binary counting system. Binary is used in electronic circuits and software programs to signal switches to turn ‘ON’ and ‘OFF’.

*Themes: series, binary, logic*

Curriculum links: Mathematics – numbers, fractions and operations. Physics – information and communication technology

**Four Colour Puzzle** (multimedia)

Colour shapes on the touch screen so neighbouring shapes are not the same colour. It sounds simple, but it’s surprisingly stumping.

*Themes: puzzle, Four Colour Theorem*

Curriculum links: Mathematics – puzzles and number tricks

**Logic Goats**

Press a series of hoof-pedals to make three goats nod their heads in various patterns. Pressing different combinations of pedals creates a series of logic gates representing: ‘AND’, ‘NOT’, and ‘Exclusive OR’ signals in the nodding goats. Logic goats is a playful exploration of logic gates, which control input and output signals in electronic goods such as computers or transistors.

*Themes: binary, logic, logic gates*

Curriculum links: Mathematics – numbers, fractions and operations. Physics – information and communication technology

**Giant Cube Dissection** (Mega Maths Floor Puzzle)

Build a giant cube using the seven pieces provided. This Soma Cube puzzle’s first challenge is to use seven different cube-based puzzle pieces to build a giant cube. You can also try building other suggested structures using the same seven puzzle pieces.

*Themes: puzzle*

Curriculum links: Mathematics – geometry and topology

**Mechanical Monkey**

Can this monkey do math? Move the mechanical monkey’s feet to numbers along the baseline and watch the monkey’s hands reveal the answer to your chosen mathematical operation. The monkey can perform operations such as addition, multiplication and exponentiation (indices) if it’s given enough bananas and time.

*Themes: arithmetic, patterns, geometry*

Curriculum links: Mathematics – statistics, probability and chance

**Meissner Solids**

Roll a square plate on top of different-shaped solids, including Reuleaux tetrahedra and Meissner solids. You can feel which shapes allow the plate to roll smoothly. Although these shapes appear to be irregular, the plate rolls smoothly due to the shapes’ constant widths.

*Themes: geometry, diameter, Meissner solids*

Curriculum links: Mathematics – geometry and topology

**Seven Bridges and Eight Bridges**

Move through the town crossing every bridge. A classic puzzle which challenges you to trace a continuous route through a town that crosses every bridge exactly once. Try the puzzle with seven bridges first, then with eight bridges. The trick is the number of nodes and edges that can be overlaid onto the map.

*Themes: puzzle, problem solving, networks, nodes*

Curriculum links: Mathematics – geometry and topology, puzzles and number tricks

**Tetrahedron**

Make a triangular-based pyramid. Sounds simple but you only have two identical pieces which must fit together to form a solid triangular-based pyramid with four faces (a tetrahedron).

*Themes: puzzle, geometry*

Curriculum links: Mathematics – geometry and topology

**Penney’s Game**

Should you go first or second? Penney’s Game challenges you to consider whether it’s best to go first or second in a game of chance. You must predict via touch screen the order in which balls will be sampled from a barrel, then the computer will also predict a sequence before balls are randomly and physically sampled.

*Themes: probability, sampling, sequences, Penney’s game, chance*

Curriculum links: Mathematics – statistics, probability and chance

**Tower of Brahma**

Can you solve the puzzle in a minimum number of moves? You must relocate a stack of five discs onto another peg, following two rules: move one disc at a time and do not place a larger disc on top of a smaller disc.

*Themes: puzzle, logic*

Curriculum links: Mathematics – puzzles and number tricks

**Conic Sections**

Hold various panels printed with the graph of a circle, hyperbola, parabola or ellipse over a spinning light and see how each curved shape can be found within the cone of light.

*Themes: conics, shapes, geometry, parabola, hyperbola, ellipse*

Curriculum links: Mathematics – geometry and topology

**Trigonometry Trammel**

Turn the handle and pointers labelled ‘sin’ and ‘cos’ will automatically work out these trigonometric functions. This elegant mechanical device allows you to physically explore angles as the ratio of lengths of triangles’ legs.

*Themes: trigonometry, geometry, triangles, measurement*

Curriculum links: Mathematics – geometry and topology

**Shortest Journey** (multimedia)

Can you find the shortest path to travel to every city on a map, starting and finishing in Canberra?

*Themes: puzzle logic*

Curriculum links: Mathematics – puzzles and number tricks, measurement (time, size, mass, density, volume)

**River Crossing** (multimedia)

Use the touch screen to move four robbers across a bridge to the opposite river bank. You must follow certain rules such as only moving one or two robbers at a time, finishing within ‘15 minutes’ and always making sure one robber holds a torch when they cross the bridge. These rules make the puzzle more challenging than you may expect.

*Themes: puzzle, optimisation theory*

Curriculum links: Mathematics – puzzles and number tricks

**Step Maze** (Mega Maths Floor Puzzle)

Rotate or ‘step’ oversized dividers across a maze, ensuring that the feet only step into matching coloured maze discs. What patterns do you notice and how can you plan ahead to reach the other side?

*Themes: puzzle, maze*

Curriculum links: Mathematics – puzzles and number tricks

**Tetrahedron** (Mega Maths Floor Puzzle)

Two oversized and identical puzzle pieces must be joined so they form a solid shape with four faces (a tetrahedron).

*Themes: puzzle, geometry*

Curriculum links: Mathematics – puzzles and number tricks

**Tower of Brahma** (Mega Maths Floor Puzzle)

Can you solve the puzzle in a minimum number of moves? You must relocate a stack of four oversized discs onto another peg, following two rules: move one disc at a time and do not place a larger disc on top of a smaller disc.

*Themes: puzzle, logic*

Curriculum links: Mathematics – puzzles and number tricks

**Maths Puzzles** (Maths puzzle placemats)

Sixty different maths puzzles have been printed onto placemat-sized panels, so you can sit at a table and solve as many different puzzles as your brain and patience will allow.

The puzzles cover a wide variety of topics including: counting; patterns; logic; problem solving; addition; multiplication; subtraction; area; shapes and other magnificently mathematical content

*Various mathematical topics including: mathematics, maths, puzzles, problem solving, arithmetic, area, patterns*

Some exhibits may not be available every day.

*Mathamazing*. Developed by Questacon – The National Science and Technology Centre, Canberra.