Loci with Cabri Geometry II Plus

An intersection with a locus
Cabri Geometry II Plus is also capable of representing intersections with loci.   The example shows a cardioid, the locus of point p with m varying around the circle.We can thus build the intersections of the curve with a small circle, centered about p, and thus obtain a good estimate of the tangent and normal of the curve p.

Displaying loci
Loci are displayed using a new, adaptive monitoring, algorithm, which returns the optimal resolution for display and printing with no further operator intervention.

A locus from a point on a mark
A construction involving a point on a grid or axe can be used to generate a locus. This locus is the set of points around the target object with the moving point tracing around all points on the grid.Such a locus can be used to explore scalar or vectorial fields.In the following example a point on a grid is associated with a circle, the radius of which is proportional to the value of a polynomial P in x & y. Then the locus of these circles is built and we obtain a visualization of the scalar field corresponding to the polynomial, thus an idea of the shape of the curve P(x,y)=0.

Algebraic Equation Curves
The ‘Coordinates or Equation’ tool can now be used for loci. The equations are determined by digital methods as algebraic curves of up to and including degree 6. If the equation of a locus is considered to exceed this functional range, the equation cannot be determined. The calculations are carried out to the precision of the machine itself (64 bits), thus numerical errors may appear.The following example shows the equation of an asteroid in a circle.

Saving a session
‘Session’ is used to save and print stages of a construction, and,therefore to analyze the behavior of offshoots during the resolution of a problemusing Cabri Geometry II Plus.
Export figure for calcs…
Cabri Geometry II Plus is capable of reading and saving drawings in Cabri® Jr format. (Menu ‘File – Open or Export figure for calcs…’)

The Cabri® Jr. interactive geometry software developed by Cabrilog for Texas Instruments is available on the TI-84 Plus and 83 Plus (SE Inclusive).