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PLThe Magic Slice! 🍦📐 (All Conic Sections in 20 Seconds)
If you also want to create animations like this for your projects, my short handbook will be very helpful for you. The link is in the bio.
What do a falling basketball, the orbit of the Earth, and the cooling towers of a nuclear power plant have in common? 🤯
By taking a "Double Cone" and slicing it with a flat plane at different angles, you can create every fundamental shape in geometry.
1. The Perfect Circle ⭕
Slice the cone perfectly horizontal. Every point is exactly the same distance from the center. It’s the ultimate symbol of symmetry!
2. The Ellipse (The Squashed Circle) 🥚
Tilt that slice just a little bit. This is the path the Earth takes around the Sun. It has two focus points, and the sum of the distances to them is always constant!
3. The Parabola (The Arc) 🏹
Tilt the slice until it is perfectly parallel to the side of the cone. This is the curve of a fountain or a kicked football.
Vertical Parabola: Opens up or down (like a U).
Horizontal Parabola: Opens left or right (like a C).
4. The Hyperbola (The Double Curve) ⚡
Slice it steep enough to hit both the top and bottom cones. You get two separate curves facing away from each other!
Rectangular Hyperbola: A special version where the curves fit perfectly inside a 90-degree corner.
The "Degenerate" Secrets: 🤫
What happens if you slice exactly through the tip (Vertex) of the cone?
Point: If the plane just touches the very center.
Straight Line: If the plane lies perfectly against the edge.
Intersecting Lines: If the plane slices vertically right through the middle.
Parallel Lines: A special case where the cone is infinitely far away!
From the smallest atom to the largest galaxy, the universe is written in Conic Sections. Which one is your favorite? 👇
Conic Sections Explained, Circle vs Ellipse, Parabola and Hyperbola, Geometry Visuals, Double Cone Model, Pre-Calculus Basics, Orbits and Physics, Degenerate Conics, Rectangular Hyperbola, Math for Engineers, Plotlab01.
#Geometry #MathVisuals #Calculus #PhysicsFacts #STEMEducation
@plotlab01
