# Potential benefits of appropriate technology use

### Generative tools for constructing one's further mathematics study.

Centers of a triangle

Centroid, Orthocenter, Circumcenter, Incenter, Euler line
Medial triangle, Orthic Triangle, Triangle from Midpoints of Orthocenter/vertex segments
Nine Point Circle

Locus Explorations

Travels in 1992 with Bill (Orthocenter), George (Centroid), and Ross (Circumcenter)

Orthotravels. What is the locus of the orthocenter when one side of a triangle is fixed and the
third vertex is moved along some path?

Extended Concurrencies of the Triangle

Fermat points, Napoleon points, and others.
Kiepert hyperbola.

Pedal Points and Pedal Triangles

Pedal.gsp. Open the file, hide the perpendiculars and move point P anywhere in the plane.
Trace the lines defining PQR as P is moved in a circle.
Trace the lines defining PQR as P is moved around the Circumcircle of ABC. (
Pedal1.gsp)
Trace the center points of PQ, QP, and QR as P is moved in a circlular path.

Squares. What is the ratio of areas of the two squares?

Conics

Parabola, Ellipse, Hyperbola: Directrix is a line or circle.

Second order conics: Directrix is a conic.

GSP Lessons

Inscribe a parabola in a triangle. GSP Sketch.

Problems. The Web Site for my Mathematical Problem Solving Course.

Folium of DeCartes -- and what if?

Folium

Translation to (x - a, y - b)

Transform to (sin x, siny)

Solve: ABC = 4; 3A + 2B - C = 3

Investigate

Graph PacMan