Search by Topic

Resources tagged with Mathematical reasoning & proof similar to Double Angle Triples:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 182 results

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

problem icon

Our Ages

Stage: 4 Challenge Level: Challenge Level:1

I am exactly n times my daughter's age. In m years I shall be ... How old am I?

problem icon

Euclid's Algorithm II

Stage: 5

We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.

problem icon

Exhaustion

Stage: 5 Challenge Level: Challenge Level:1

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

problem icon

Proof Sorter - Geometric Series

Stage: 5 Challenge Level: Challenge Level:1

This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.

problem icon

Proof Sorter - Quadratic Equation

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

problem icon

To Prove or Not to Prove

Stage: 4 and 5

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

problem icon

Never Prime

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

problem icon

Encircling

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?

problem icon

Direct Logic

Stage: 5 Challenge Level: Challenge Level:1

Can you work through these direct proofs, using our interactive proof sorters?

problem icon

Dalmatians

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

problem icon

Napoleon's Hat

Stage: 5 Challenge Level: Challenge Level:1

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

problem icon

Whole Number Dynamics IV

Stage: 4 and 5

Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?

problem icon

The Frieze Tree

Stage: 3 and 4

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

problem icon

Whole Number Dynamics I

Stage: 4 and 5

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

problem icon

The Triangle Game

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you discover whether this is a fair game?

problem icon

Matter of Scale

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Prove Pythagoras' Theorem using enlargements and scale factors.

problem icon

Proof Sorter - Sum of an AP

Stage: 5 Challenge Level: Challenge Level:1

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

problem icon

Always Perfect

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

problem icon

Ordered Sums

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .

problem icon

Diophantine N-tuples

Stage: 4 Challenge Level: Challenge Level:1

Can you explain why a sequence of operations always gives you perfect squares?

problem icon

Euler's Squares

Stage: 4 Challenge Level: Challenge Level:1

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

problem icon

Pythagoras Proofs

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make sense of these three proofs of Pythagoras' Theorem?

problem icon

Kite in a Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make sense of the three methods to work out the area of the kite in the square?

problem icon

More Dicey Decisions

Stage: 5 Challenge Level: Challenge Level:1

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

problem icon

Classifying Solids Using Angle Deficiency

Stage: 3 and 4 Challenge Level: Challenge Level:1

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

problem icon

Fractional Calculus III

Stage: 5

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

problem icon

Impossible Sandwiches

Stage: 3, 4 and 5

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.

problem icon

Continued Fractions II

Stage: 5

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

problem icon

On the Importance of Pedantry

Stage: 3, 4 and 5

A introduction to how patterns can be deceiving, and what is and is not a proof.

problem icon

Dodgy Proofs

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

These proofs are wrong. Can you see why?

problem icon

Interpolating Polynomials

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

problem icon

Euler's Formula and Topology

Stage: 5

Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the. . . .

problem icon

Mediant

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.

problem icon

Number Rules - OK

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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...

problem icon

Square Pair Circles

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

Mouhefanggai

Stage: 4

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

problem icon

A Computer Program to Find Magic Squares

Stage: 5

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.

problem icon

Proofs with Pictures

Stage: 5

Some diagrammatic 'proofs' of algebraic identities and inequalities.

problem icon

Modulus Arithmetic and a Solution to Dirisibly Yours

Stage: 5

Peter Zimmerman from Mill Hill County High School in Barnet, London gives a neat proof that: 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.

problem icon

Advent Calendar 2011 - Secondary

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

problem icon

More Sums of Squares

Stage: 5

Tom writes about expressing numbers as the sums of three squares.

problem icon

Particularly General

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

By proving these particular identities, prove the existence of general cases.

problem icon

Whole Number Dynamics V

Stage: 4 and 5

The final of five articles which containe the proof of why the sequence introduced in article IV either reaches the fixed point 0 or the sequence enters a repeating cycle of four values.

problem icon

Telescoping Functions

Stage: 5

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.

problem icon

A Knight's Journey

Stage: 4 and 5

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.

problem icon

Whole Number Dynamics III

Stage: 4 and 5

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

problem icon

Pythagorean Triples II

Stage: 3 and 4

This is the second article on right-angled triangles whose edge lengths are whole numbers.

problem icon

Can it Be

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

problem icon

Whole Number Dynamics II

Stage: 4 and 5

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

problem icon

Where Do We Get Our Feet Wet?

Stage: 5

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