Other tags that relate to Square Pizza
Generalising. Describing patterns and sequences. Creating and manipulating expressions and formulae. Mathematical reasoning & proof. Visualising. Symmetry. Pythagoras' theorem. Factors and multiples. Interactivities. Area - triangles, quadrilaterals, compound shapes.There are 74 results
Broad Topics > Pythagoras and Trigonometry > Pythagoras' theorem
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?
Tilted Squares
Age 11 to 14
Challenge Level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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.
Kite in a Square
Age 14 to 16
Challenge Level
Can you make sense of the three methods to work out the area of the kite in the square?
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.
Matter of Scale
Age 14 to 16
Challenge Level
Prove Pythagoras' Theorem using enlargements and scale factors.
Pythagorean Triples I
Age 11 to 16
The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!
Pythagorean Triples II
Age 11 to 16
This is the second article on right-angled triangles whose edge lengths are whole numbers.
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?
Weighty Problem
Age 11 to 14
Challenge Level
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
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. . . .
Cutting a Cube
Age 11 to 14
Challenge Level
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Tilting Triangles
Age 14 to 16
Challenge Level
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
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?
The Spider and the Fly
Age 14 to 16
Challenge Level
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
All Tied Up
Age 14 to 16
Challenge Level
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
Corridors
Age 14 to 16
Challenge Level
A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
Pythagoras Proofs
Age 14 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
Circle Box
Age 14 to 16
Challenge Level
It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
Garden Shed
Age 11 to 14
Challenge Level
Can you minimise the amount of wood needed to build the roof of my garden shed?
Liethagoras' Theorem
Age 7 to 14
Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.
Star Gazing
Age 14 to 16
Challenge Level
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
Where to Land
Age 14 to 16
Challenge Level
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
The Fire-fighter's Car Keys
Age 14 to 16
Challenge Level
A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.
Nicely Similar
Age 14 to 16
Challenge Level
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Grid Lockout
Age 14 to 16
Challenge Level
What remainders do you get when square numbers are divided by 4?
Under the Ribbon
Age 14 to 16
Challenge Level
A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?
Napkin
Age 14 to 16
Challenge Level
A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .
The Pillar of Chios
Age 14 to 16
Challenge Level
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
Zig Zag
Age 14 to 16
Challenge Level
Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
The Medieval Octagon
Age 14 to 16
Challenge Level
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Trice
Age 11 to 14
Challenge Level
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
Where Is the Dot?
Age 14 to 16
Challenge Level
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
The Old Goats
Age 11 to 14
Challenge Level
A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .
Isosceles
Age 11 to 14
Challenge Level
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
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.
Three Four Five
Age 14 to 16
Challenge Level
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
A Chordingly
Age 11 to 14
Challenge Level
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
Six Discs
Age 14 to 16
Challenge Level
Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?
Crescents and Triangles
Age 14 to 16
Challenge Level
Can you find a relationship between the area of the crescents and the area of the triangle?
Holly
Age 14 to 16
Challenge Level
The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.
Squareo'scope Determines the Kind of Triangle
Age 11 to 14
A description of some experiments in which you can make discoveries about triangles.
Inscribed in a Circle
Age 14 to 16
Challenge Level
The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?
Ball Packing
Age 14 to 16
Challenge Level
If a ball is rolled into the corner of a room how far is its centre from the corner?
Medallions
Age 14 to 16
Challenge Level
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
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.
Two Circles
Age 14 to 16
Challenge Level
Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?
Are You Kidding
Age 14 to 16
Challenge Level
If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?
Take a Square
Age 14 to 16
Challenge Level
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
NRICH is part of the family of activities in the Millennium Mathematics Project.