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Conics Materials
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1. Conics Applets
- Seções cônicas e elementos das curvas cônicas
- Conic cone section
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2. What-If-Not Conic Constructions GGG 2017
- What-If-Not Conic Constructions #1
- The Art of Problem Posing
- What-If-Not Conic Constructions #2
- What-If-Not Conic Constructions #3
- What-If-Not Conic Constructions #4
- What-If-Not Conic Construction #5
- What-If-Not Side-By-Side Construction
- What-If-Not Conic Constructions #6
- Conic Constructions Using Other Directrix
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3. Polar reciprocation
- Polar Reciprocation
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Conics Materials
Bruno Leite, Jul 26, 2017
In this Book I am collecting some Conic's Geogebra materials that I consider interesting.
Table of Contents
- Conics Applets
- Seções cônicas e elementos das curvas cônicas
- Conic cone section
- What-If-Not Conic Constructions GGG 2017
- What-If-Not Conic Constructions #1
- The Art of Problem Posing
- What-If-Not Conic Constructions #2
- What-If-Not Conic Constructions #3
- What-If-Not Conic Constructions #4
- What-If-Not Conic Construction #5
- What-If-Not Side-By-Side Construction
- What-If-Not Conic Constructions #6
- Conic Constructions Using Other Directrix
- Polar reciprocation
- Polar Reciprocation
Seções cônicas e elementos das curvas cônicas
Glossário
gº - Ângulo entre eixo (e) e geratriz (g);
pº - Ângulo entre eixo (e) e plano de seção (p);
p - Plano de seção;
sc - Seção cônica;
e - Eixo da superficie cônica;
P - Ponto da curva cônica;
g - Geratriz da superfície cônica;
g// - Plano paralelo ao plano de seção (p) passante pelo vértice do cone (V);
rcc e rmd - reta de cota constante e de máximo declive do plano de seção em relação ao plano xy;
V1 e V2 - Vértices do eixo principal da cônica;
V3 e V4 - Vértices do eixo secundário da cônica;
e1 e e2 - Esferas tangentes à superfície cônia e ao plano de seção;
F1 e F2 - Focos das curvas cônicas (e pontos de tangências das esferas com o plano de seção);
p1 e p2 - Planos diretores determinados pelas pelas circunferências de tangência das esferas com a superfície cônica;
d1 e d2 - Retas diretrizes das curvas cônicas determinadas pelas interseções dos planos diretores (p1 e p2) e o plano de seção (p);
r1 e r2 - Raios focais (distâncias entre P e os focos);
Exc. - Excentrididade;
cd1 e cd2 - Círculos diretores;
t - Tangente à cônica em P;
t1, t2, t3 e t4 - Tangentes nos vértices da curva;
C - Centro interno;
Ce - Centro externo.
What-If-Not Conic Constructions GGG 2017
This is a collection of investigations that explore small changes to the traditional conic constructions for the GeoGebra Global Gathering 2017
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1. What-If-Not Conic Constructions #1
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2. The Art of Problem Posing
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3. What-If-Not Conic Constructions #2
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4. What-If-Not Conic Constructions #3
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5. What-If-Not Conic Constructions #4
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6. What-If-Not Conic Construction #5
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7. What-If-Not Side-By-Side Construction
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8. What-If-Not Conic Constructions #6
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9. Conic Constructions Using Other Directrix
What-If-Not Conic Constructions #1
The Parabola Construction
We begin with the construction of a parabola. Play through the construction. Drag the points so you understand how the parts of the construction behave.
A parabola is the locus of all points equidistant from a point and a line. We can also discuss eccentricity which is the ratio of the these two distances
Distance[F,P]:Distance[P,D].
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There are four construction characteristics that might be interesting to investigate.
- What happens if the perpendicular bisector is perpendicular, but is not a bisector?
- What happens if the perpendicular bisector is a bisector, but is not perpendicular?
- What happens if the perpendicular to the directrix constructed at D is not perpendicular?
- What happens if the directrix is not a line?
Polar Reciprocation
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