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LOCI Main Menu
A. Sketching Paths of Points This section produces diagrams for some well known and some less well known loci. Getting a feel for what loci are possible.
B Paths and InstructionsA list of instructions are given in each case.Choose which shape the instructions describe!
Introduction: Some real life loci for discussion
1 2 3 4 5 6 7 8 9 10
1 2List the instructions:
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LOCI The golf ball:
A golf ball is driven on to the green. The ball bounces several times and drops into the hole.
Imagine the path of the ball.
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LOCI Imagine the path of the ball.
For the following examples trace out the path with your hands.
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LOCI Think about the loci and discuss.
A helicopter takes off rises to a height of 100 ft. It accelerates forward and rises to 3000 ft where it levels out then continues on its way.
Picture in 2-D and 3-D ??
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LOCI
A nervous man paces up and down in one of the capsules on the Millennium Eye as he “enjoys” the view.
Picture in 2-D and 3-D ??
Think about the loci and discuss.
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A man has been out for the evening, has locked himself out of his flat and has to climb the spiral fire escape. (What if he is drunk?)
Picture in 2-D and 3-D ??
Think about the loci and discuss.
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A fighter plane takes off from a runway which runs West-East. Imagine its path if it wants to head ... North ... West
Picture in 2-D and 3-D ??
Think about the loci and discuss.
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Imagine a pendulum ... not that simple! A distressed mouse runs up and down the pendulum.
Picture in 2-D and 3-D ??
Think about the loci and discuss.
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A railway track is built so as to reduce the gradient a train has to travel through the mountains. Climbing south to north a “curved / circular loop” tunnel is built into the mountain before the train continues on its way
Picture in 2-D and 3-D ??
Think about the loci and discuss.
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A Path between two Points
“A ship sails between two lighthouses A and B so that its distance from and and from B is the same. B is 10km due East of A. Sketch the locus of the ship”
A B
N
Press P to undo “locus”
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A Path between two Points
X
YN
“Airport X is SE of airport Y and 100km away. A plane flies such that its path is EQUIDISTANT from X and Y Sketch the locus of the plane”
Press P to undo “locus”
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The PERPENDICULAR BISECTOR
P
Q
This path is called the “perpendicular bisector” of AB Perpendicular ... because it cuts AB at RIGHT ANGLESBisector ... because it cuts AB exactly in half.
Press P to undo “locus”
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A Path between two Lines
“Two walls meet at a point X, forming an acute angle. A boy stands as close to X as possible and then walks away from the corner in such a way as to keep the same distance from both walls. Sketch his path.
X
Press P to undo “locus”
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The ANGLE BISECTOR
This path cuts the angle exactly in half and at all times remains equidistant from the two lines that meet at a particular point.
Press P to undo “locus”
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Equidistant from a Point
Sketch the locus of points which are a constant distance from a point P.
P
Press P to undo “locus”
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Another “equidistant” locus.
“A spatially aware beetle walks around a pencil on a table. It keeps the same distance from the pencil”
Press P to undo “locus”
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The path of a “golf ball”?
“A golf ball is lofted on to the green. Sketch it’s path as it bounces towards the hole.
Press P to undo “locus”
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Instructions ... WHICH SHAPE?
A CB D
EXAMPLE
Forward 6, Turn + 90o, Forward 8, Turn + 90o,Forward 6, Turn + 90o,Forward 8.
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Instructions ... WHICH SHAPE? 1
A CB D
Forward 5, Turn + 45o,Forward 5, Turn + 45o, Forward 5, Turn + 45o,Forward 5, Turn + 45o, Forward 5, Turn + 45o, Forward 5, Turn + 45o,Forward 5, Turn + 45o,Forward 5.
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Instructions ... WHICH SHAPE? 2
A CB D
Forward 6, Turn + 120o, Forward 6, Turn + 120o,Forward 6.
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Instructions ... WHICH SHAPE? 3
A CB D
Forward 6,Turn +103.3o, Forward 13,Turn +153.3o, Forward 13.
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Instructions ... WHICH SHAPE? 4
A CB D
Forward 5, Turn + 60o, Forward 5, Turn + 60o, Forward 5, Turn + 60o,Forward 5, Turn + 60o,Forward 5, Turn + 60o, Forward 5.
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Instructions ... WHICH SHAPE? 5
A CB D
Forward 8, Turn + 90o, Forward 4, Turn + 90o, Forward 4, Turn - 90o,Forward 4, Turn + 90o,Forward 4, Turn + 90o, Forward 8.
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Instructions ... WHICH SHAPE? 6
A CB D
Forward 6, Turn + 45o,Forward 4, Turn + 45o, Forward 2, Turn + 45o,Forward 4, Turn + 45o, Forward 6, Turn + 45o, Forward 4, Turn + 45o,Forward 2, Turn + 45o,Forward 4.
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Instructions ... WHICH SHAPE? 7
A CB D
Forward 8, Turn + 90o, Forward 4, Turn + 53.1o, Forward 5, Turn + 73.8o,Forward 5, Turn + 53.1o,Forward 4.
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Instructions ... WHICH SHAPE? 8
A CB D
Forward 8, Turn + 72o, Forward 8, Turn + 72o, Forward 8, Turn + 72o,Forward 8, Turn + 72o,Forward 8.
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Instructions ... WHICH SHAPE? 9
A CB D
Forward 10, Turn + 90o,Forward 8, Turn + 135o, Forward 4.95, Turn - 45o, Forward 3, Turn - 45o,Forward 4.95, Turn + 135o,Forward 8.
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Instructions ... WHICH SHAPE? 10
A CB D
Forward 6, Turn + 90o,Forward 2, Turn - 90o, Forward 4, Turn + 90o,Forward 2, Turn + 90o, Forward 6, Turn + 90o, Forward 2, Turn - 90o,Forward 4, Turn + 90o,Forward 2.
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A CB D
SHAPES List the instructions 1
STARTING DIRECTION STARTING POINT Bottom left hand corner
E GF H