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DefinitionDefinitionof Locusof Locus

Stage 6 - Year 11Stage 6 - Year 11

Mathematic(Preliminary)

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Definition of a locusDefinition of a locus Describes the path of a single moving Describes the path of a single moving

point that obeys certain conditions.point that obeys certain conditions.

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The CircleThe Circle

The point is always the same distance from the point ‘O’

O

x2 + y2 = r2

Definition of a locusDefinition of a locus Describes the path of a single moving Describes the path of a single moving

point that obeys certain conditions.point that obeys certain conditions.

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The Straight lineThe Straight line

y = mx + b

Definition of a locusDefinition of a locus Describes the path of a single moving Describes the path of a single moving

point that obeys certain conditions.point that obeys certain conditions.

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Reuleaux Triangle 1Reuleaux Triangle 1

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Reuleaux Triangle 2Reuleaux Triangle 2rotates.  First, the path of the boundary is not a square at the four corners.  But because the triangle rotates within a square, it is the basis for a square drill bit.

The behavior of the center is also fascinating.  The center does not remain fixed and thus traces a path composed of four arcs of an ellipse.

Observe the path of the triangle as it

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EllipseEllipse

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Point rotating on Point rotating on circlecircle

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The Double PendulumThe Double Pendulum

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Pedal Pedal CurveCurve A pedal curve A pedal curve

is the locus of is the locus of the feet of the the feet of the perpendiculars perpendiculars from the point from the point to the tangents to the tangents to the given to the given figure. figure.

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HypotrochoiHypotrochoid d The red curve is traced as the The red curve is traced as the

smaller black circle rolls around smaller black circle rolls around inside the larger black circleinside the larger black circle

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DartsDarts

Ballistics Simulator