Osculating Circle/Sphere

Topic:
Circle, Sphere

Osculating Circle

Let C be a space curve with three neighbooring points P,Q, R on it. Then Osculating circle at P is defined as the limiting position of the circle through P,Q,R as Q,R approaches to P. Mathematically, Osculating circle at P= circle through P,Q,R

Osculating Sphere

Let C be a space curve with three neighbooring points P,Q, R,S on it. Then Osculating sphere at P is defined as the limiting position of the sphere PQRS as Q,R,S approaches to P. Mathematically, Osculating sphere at P= sphere through P,Q,R,S

Relation between Osculating circle and Osculating Sphere

In a space curve, what is the relation between the center of osculating circle and center of osculating sphere ? To answer this question Slide the parameter (t) given left in the applet below, and see the effect in 3D graph on the right. Space curve मा, osculating circle को center र osculating sphere को center को सम्बन्ध के हुन्छ ? यस प्रश्नको उतर को लागी, तलको Applet मा बायाँ तिर को Slider (t) लाई चलाउनुहोस र यसको असर दायाँ तिरको 3D चित्रमा हेर्नुहोस । र यस applet को अन्तमा भएको प्रश्नको उतर दिनुहोस ।

Test your Understanding

In which of the following case, the center of osculating circle and center of osculating sphere do coincide?

Check your answer here