Other tags that relate to Trig Reps
Sine, cosine, tangent. Regular polygons and circles. Trigonometric functions and graphs. Maths Supporting SET. Generalising. Maclaurin series. Pythagoras' theorem. Complex numbers. Investigations. Trigonometric identities.There are 77 results
Broad Topics > Thinking Mathematically > Generalising
Ball Bearings
Age 16 to 18
Challenge Level
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Shape and Territory
Age 16 to 18
Challenge Level
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
Chord
Age 16 to 18
Challenge Level
Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.
Why Stop at Three by One
Age 16 to 18
Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.
Incircles
Age 16 to 18
Challenge Level
The incircles of 3, 4, 5 and of 5, 12, 13 right angled triangles have radii 1 and 2 units respectively. What about triangles with an inradius of 3, 4 or 5 or ...?
Squaring the Circle and Circling the Square
Age 14 to 16
Challenge Level
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
In a Spin
Age 14 to 16
Challenge Level
What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
Equilateral Areas
Age 14 to 16
Challenge Level
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
Cyclic Triangles
Age 16 to 18
Challenge Level
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
Semi-square
Age 14 to 16
Challenge Level
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
Pareq Calc
Age 14 to 16
Challenge Level
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
Generating Triples
Age 14 to 16
Challenge Level
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Pick's Theorem
Age 14 to 16
Challenge Level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Square Pizza
Age 14 to 16
Challenge Level
Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
Fractional Calculus II
Age 16 to 18
Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.
Fractional Calculus I
Age 16 to 18
You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.
Magic Squares
Age 14 to 18
An account of some magic squares and their properties and and how to construct them for yourself.
Of All the Areas
Age 14 to 16
Challenge Level
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Multiplication Square
Age 14 to 16
Challenge Level
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Polycircles
Age 14 to 16
Challenge Level
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Pinned Squares
Age 14 to 16
Challenge Level
What is the total number of squares that can be made on a 5 by 5 geoboard?
A Tilted Square
Age 14 to 16
Challenge Level
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
For Richer for Poorer
Age 14 to 16
Challenge Level
Charlie has moved between countries and the average income of both has increased. How can this be so?
Pair Products
Age 14 to 16
Challenge Level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Mystic Rose
Age 14 to 16
Challenge Level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Sliding Puzzle
Age 11 to 16
Challenge Level
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Winning Lines
Age 7 to 16
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Can it Be?
Age 16 to 18
Challenge Level
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
Nim
Age 14 to 16
Challenge Level
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Searching for Mean(ing)
Age 11 to 16
Challenge Level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Generally Geometric
Age 16 to 18
Challenge Level
Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.
Multiplication Arithmagons
Age 14 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Sums of Pairs
Age 11 to 16
Challenge Level
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Take Three from Five
Age 11 to 16
Challenge Level
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Harmonic Triangle
Age 14 to 16
Challenge Level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Plus Minus
Age 14 to 16
Challenge Level
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Interpolating Polynomials
Age 16 to 18
Challenge Level
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.
More Twisting and Turning
Age 11 to 16
Challenge Level
It would be nice to have a strategy for disentangling any tangled ropes...
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
Irrational Arithmagons
Age 16 to 18
Challenge Level
Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
Partly Painted Cube
Age 14 to 16
Challenge Level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Odd Differences
Age 14 to 16
Challenge Level
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Games Related to Nim
Age 5 to 16
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Pentanim
Age 7 to 16
Challenge Level
A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
NRICH is part of the family of activities in the Millennium Mathematics Project.