May 10, 2013 and May 18 - May 28, 2015
Treasure Hunt Experience Closure Reflection
What did we discover in looking for treasure?
In each treasure hunt experience we were given a set of conditions to help us find where our treasure could be. We found a collection of locations which satisfied the conditions and these points would form circles, lines or other curves such as a parabola, ellipse and hyperbola. What we discovered is called a locus of points.
A locus of points is a collection of points, all of which satisfy some specific condition.
Big Idea: Loci ( plural of locus is pronounced “low sigh”) is essentially the study of curves.
Our locus was a collection of locations where our treasure could be.
- The Circle
The treasure is 100 feet from a tree in a field. Where can the treasure be?
The locus of points that are a set distance from a given point A is a circle.
- Two Parallel Lines
The treasure is buried 100 feet from a straight fence in a field
The locus of points that are a set distance from a given line A is two parallel lines, one on each side of the given line.
- Two Concentric Circles
The treasure is buried 100 feet from a circular fence in a field.
The locus of points that are a set distance from a given circle is two circles, one on each side of the given circle.
- A Perpendicular Bisector
The treasure is buried so that it is equally distant from 2 trees in a field.
The locus of points equidistant from two points is the perpendicular bisector of the line segment that joins the two given points.
- Two Angle Bisectors
The treasure is buried equally distant from two straight fences which intersect each other at a random angle in the field.
The locus of points equidistant from two intersecting lines is the two angle bisectors of the given lines.
- The Parabola
The treasure is buried an equal distance from a tree and a straight fence and the tree is not on the straight fence. We need to survey the field for this one!
The locus of points equidistant from a point and a straight line is a parabola.
- The Ellipse
The treasure is buried equally distant from a tree planted inside a circular fence and the circular fence. We need to survey the field with 1 cm. concentric circles inside the circular fence and 1 cm. concentric circles around the tree to help us find this one!
The locus of points equidistant from a given circle and a point inside the circle is an ellipse.
- The Hyperbola
The treasure is buried equally distant from two trees which are planted equally
distant from a circular fence in the middle of a field, and equally distant from the fence.
The locus of points equidistant from a circle and two points equidistant from the circle is a hyperbola.