menu © boardworks ltd 2001 loci. menu © boardworks ltd 2001 loci main menu a.sketching paths of...

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© Boardworks Ltd 2001

Loci

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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 Paths mapped out by sets of points.

Imagine you are the point…

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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.


Think about the loci and discuss.

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LOCI

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?)



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LOCI

A fighter plane takes off from a runway which runs West-East. Imagine its path if it wants to head ... North ... West



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LOCI

Imagine a pendulum ... not that simple! A distressed mouse runs up and down the pendulum.



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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



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LOCIA. Sketching the paths of points

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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”


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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.


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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


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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.


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Equidistant from a Point

Sketch the locus of points which are a constant distance from a point P.

P


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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”


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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.


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LOCIB. Instructions for Producing Shapes

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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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A CB D

Forward 6, Turn + 120o, Forward 6, Turn + 120o,Forward 6.

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A CB D

Forward 6,Turn +103.3o, Forward 13,Turn +153.3o, Forward 13.

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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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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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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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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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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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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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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

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A CB D

SHAPES List the instructions 2

STARTING DIRECTION STARTING POINT Bottom left hand corner

E GF H

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