Resources tagged with Circles similar to Curved Square:
Other tags that relate to Curved Square
Integration. Integration by substitution. Calculus generally. Pythagoras' theorem. Maths Supporting SET. Circles. Inequality/inequalities. Coordinates. Cartesian equations of circles. Differentiation.There are 58 results
Broad Topics > 2D Geometry, Shape and Space > Circles
Approximating Pi
Stage: 4 and 5 Challenge Level: 
By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
Retracircles
Stage: 5 Challenge Level:
Four circles all touch each other and a circumscribing circle. Find the ratios of the radii and prove that joining 3 centres gives a 3-4-5 triangle.
What Is the Circle Scribe Disk Compass?
Stage: 3 and 4
Introducing a geometrical instrument with 3 basic capabilities.
Round and Round
Stage: 4 Challenge Level:
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
Orthogonal Circle
Stage: 5 Challenge Level:
Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.
Logosquares
Stage: 5 Challenge Level:
Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
Circle Packing
Stage: 4 Challenge Level:
Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...
Fitting In
Stage: 4 Challenge Level:
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .
Baby Circle
Stage: 5 Challenge Level:
A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?
2D-3D
Stage: 5 Challenge Level:
Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of. . . .
A Rational Search
Stage: 4 and 5 Challenge Level:
Investigate constructible images which contain rational areas.
Lunar Angles
Stage: 5 Challenge Level:
What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?
Salinon
Stage: 4 Challenge Level:
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Circles in Circles
Stage: 5 Challenge Level:
This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.
Arclets Explained
Stage: 3 and 4
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
Squaring the Circle and Circling the Square
Stage: 4 Challenge Level:
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Spokes
Stage: 5 Challenge Level:
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
Circumnavigation
Stage: 4 Challenge Level:
The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
Semi-detached
Stage: 4 Challenge Level:
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
LOGO Challenge 11 - More on Circles
Stage: 3 and 4 Challenge Level:
Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .
Curvy Areas
Stage: 4 Challenge Level:
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Ford Circles
Stage: 5 Challenge Level:
Small circles nestle under touching parent circles when they sit on the axis at neighbouring points in a Farey sequence.
Track Design
Stage: 4 Challenge Level:
Where should runners start the 200m race so that they have all run the same distance by the finish?
Witch's Hat
Stage: 3 and 4 Challenge Level:
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Gym Bag
Stage: 3 and 4 Challenge Level:
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Partly Circles
Stage: 4 Challenge Level:
What is the same and what is different about these circle questions? What connections can you make?
LOGO Challenge 12 - Concentric Circles
Stage: 3 and 4 Challenge Level:
Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.
Spirostars
Stage: 5 Challenge Level:
A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
Link Puzzle
Stage: 2, 3 and 4 Challenge Level:
A metal puzzle which led to some mathematical questions.
First Forward Into Logo 4: Circles
Stage: 2, 3 and 4 Challenge Level:
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Roaming Rhombus
Stage: 4 Challenge Level:
We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .
Get Cross
Stage: 4 Challenge Level:
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
Escriptions
Stage: 5 Challenge Level:
For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
Illusion
Stage: 3 and 4 Challenge Level:
A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?
Some(?) of the Parts
Stage: 4 Challenge Level:
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
Quadarc
Stage: 4 Challenge Level:
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .
Circumspection
Stage: 4 Challenge Level:
M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.
Kissing
Stage: 5 Challenge Level:
Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
Just Touching
Stage: 5 Challenge Level:
Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
Ball Bearings
Stage: 5 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.
Area I'n It
Stage: 5 Challenge Level:
Triangle ABC has altitudes h1, h2 and h3. The radius of the inscribed circle is r, while the radii of the escribed circles are r1, r2 and r3 respectively. Prove: 1/r = 1/h1 + 1/h2 + 1/h3 = 1/r1 +. . . .
Three Four Five
Stage: 4 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.
Holly
Stage: 4 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.
A Rolling Disc - Periodic Motion
Stage: 5
Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?
LOGO Challenge 10 - Circles
Stage: 3 and 4 Challenge Level:
In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.
Like a Circle in a Spiral
Stage: 2, 3 and 4 Challenge Level:
A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
Rolling Coins
Stage: 4 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. . . .
Circles in Quadrilaterals
Stage: 4 Challenge Level:
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
NRICH is part of the family of activities in the Millennium Mathematics Project.