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Resources tagged with Mathematical reasoning & proof similar to Stonehenge:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof

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Stonehenge

Age 16 to 18 Challenge Level:

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

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Logic, Truth Tables and Switching Circuits

Age 11 to 18

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.

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Logic, Truth Tables and Switching Circuits Challenge

Age 11 to 18

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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Truth Tables and Electronic Circuits

Age 11 to 18

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18 Challenge Level:

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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Fractional Calculus III

Age 16 to 18

Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.

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Air Nets

Age 7 to 18 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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Proofs with Pictures

Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities.

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Iffy Logic

Age 14 to 18 Challenge Level:

Can you rearrange the cards to make a series of correct mathematical statements?

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The Triangle Game

Age 11 to 16 Challenge Level:

Can you discover whether this is a fair game?

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AMGM

Age 14 to 16 Challenge Level:

Can you use the diagram to prove the AM-GM inequality?

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Middle Man

Age 16 to 18 Challenge Level:

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?

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Contrary Logic

Age 16 to 18 Challenge Level:

Can you invert the logic to prove these statements?

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Sperner's Lemma

Age 16 to 18

An article about the strategy for playing The Triangle Game which appears on the NRICH site. It contains a simple lemma about labelling a grid of equilateral triangles within a triangular frame.

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A Computer Program to Find Magic Squares

Age 16 to 18

This follows up the 'magic Squares for Special Occasions' article which tells you you to create a 4by4 magicsquare with a special date on the top line using no negative numbers and no repeats.

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Water Pistols

Age 16 to 18 Challenge Level:

With n people anywhere in a field each shoots a water pistol at the nearest person. In general who gets wet? What difference does it make if n is odd or even?

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Picture Story

Age 11 to 16 Challenge Level:

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

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Natural Sum

Age 14 to 16 Challenge Level:

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

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Thousand Words

Age 16 to 18 Challenge Level:

Here the diagram says it all. Can you find the diagram?

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Sprouts Explained

Age 7 to 18

This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with. . . .

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Notty Logic

Age 16 to 18 Challenge Level:

Have a go at being mathematically negative, by negating these statements.

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Triangular Intersection

Age 14 to 16 Short Challenge Level:

What is the largest number of intersection points that a triangle and a quadrilateral can have?

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Dalmatians

Age 14 to 18 Challenge Level:

Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.

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To Prove or Not to Prove

Age 14 to 18

A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.

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Impossible Sandwiches

Age 11 to 18

In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.

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An Introduction to Number Theory

Age 16 to 18

An introduction to some beautiful results of Number Theory

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Rolling Coins

Age 14 to 16 Challenge Level:

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .

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Tree Graphs

Age 16 to 18 Challenge Level:

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has. . . .

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Advent Calendar 2011 - Secondary

Age 11 to 18 Challenge Level:

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

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Dodgy Proofs

Age 16 to 18 Challenge Level:

These proofs are wrong. Can you see why?

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Proximity

Age 14 to 16 Challenge Level:

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

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Yih or Luk Tsut K'i or Three Men's Morris

Age 11 to 18 Challenge Level:

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

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Picturing Pythagorean Triples

Age 14 to 18

This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.

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Proof Sorter - Sum of an AP

Age 16 to 18 Challenge Level:

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

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Converse

Age 14 to 16 Challenge Level:

Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?

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The Clue Is in the Question

Age 16 to 18 Challenge Level:

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

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More Number Sandwiches

Age 11 to 16 Challenge Level:

When is it impossible to make number sandwiches?

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Composite Notions

Age 14 to 16 Challenge Level:

A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.

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Continued Fractions II

Age 16 to 18

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

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Similarly So

Age 14 to 16 Challenge Level:

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

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Square Pair Circles

Age 16 to 18 Challenge Level:

Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.

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Where Do We Get Our Feet Wet?

Age 16 to 18

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.

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Rhombus in Rectangle

Age 14 to 16 Challenge Level:

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

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The Frieze Tree

Age 11 to 16

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

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Round and Round

Age 14 to 16 Challenge Level:

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

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Matter of Scale

Age 14 to 16 Challenge Level:

Prove Pythagoras' Theorem using enlargements and scale factors.

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Pent

Age 14 to 18 Challenge Level:

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

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Telescoping Functions

Age 16 to 18

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.

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Magic Squares II

Age 14 to 18

An article which gives an account of some properties of magic squares.

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Number Rules - OK

Age 14 to 16 Challenge Level:

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...