Divergent Series and Convergent Series Divergent Series: 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? mathematics, maths, series, sum, fractions, area, length Mathematics – geometry & topology Ellipse Release a ball so it rolls down a ramp and around an elliptically-shaped billiard table. The ball will roll into a hole at the other end of the table if it rolls over the ellipse’s focal point. mathematics, maths, ellipse, focal point, reflection Mathematics – geometry & topology Flip Flop and Digital Counter Drop a disc down through a series of flip flop gates that are stacked one above the other. 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’. mathematics, series, binary, logic Mathematics – numbers, fractions and operations Physics – information & communication technology 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. mathematics, maths, binary, logic, logic gates, Mathematics – numbers, fractions and operations Physics – information & communication technology Manacles 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. mathematics, maths, topology, problem solving, puzzle Mathematics – geometry & topology Mathematics – puzzles & number tricks
Mechanical Monkey 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. mathematics, maths, arithmetic, patterns geometry, monkeys Mathematics – statistics, probability & 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. mathematics, maths, geometry, diameter, Meissner solids Mathematics – geometry & topology Parabola Drop a ball anywhere onto a parabola-shaped dish and notice how the ball rebounds, then each time against a disc suspended above the dish (the focal point). mathematics, maths, parabola, focal point, focus, reflection, Mathematics – geometry & topology Penney’s Game 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 mathematics, maths, probability, sampling, sequences, Penney's game, chance, Mathematics – statistics, probability & chance Range Finder Find the distance to a suite of targets using two cameras and trigonometry instead of a tape measure. mathematics, maths, trigonometry, distance, measurement Mathematics – geometry & topology Seven Bridges and Eight Bridges 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. mathematics, maths, puzzle, problem solving, networks, nodes Mathematics – geometry & topology Mathematics – puzzles & number tricks