Elliptical Cross Sections

[math]\displaystyle{ \underline{\textbf{Navigation}} }[/math]

[math]\displaystyle{ \vartriangleleft }[/math] [math]\displaystyle{ \triangle }[/math] [math]\displaystyle{ \vartriangleright }[/math]

Elliptic Conic Section

If the conic is an ellipse, 0<e<1. This implies

[math]\displaystyle{ e=\frac{\sin \beta}{\sin \alpha}=\frac{\sin\ (25^{\circ})}{\sin (90^{\circ}-\theta)} }[/math]

[math]\displaystyle{ \frac{sin (25^{\circ})}{cos (\theta)}=e }[/math]

since e must be less than 1, this sets the limit of theta at less than 65 degrees. Since the limit of [math]\displaystyle{ \theta=0 }[/math], this implies the minimum eccentricity will be [math]\displaystyle{ e\approx .4291 }[/math]

This implies that the shape made on the the plane of the sector is an ellipse for angles

[math]\displaystyle{ 0<\theta<65^{\circ} }[/math]

---

[math]\displaystyle{ \underline{\textbf{Navigation}} }[/math]

[math]\displaystyle{ \vartriangleleft }[/math] [math]\displaystyle{ \triangle }[/math] [math]\displaystyle{ \vartriangleright }[/math]