[latexpage]
Relevant terminology
Generator = a linear line (green line) that intersects a vertical line called the axis at a fixed point (purple dot) called the vertex
- Note: the angle between the generator and the axis is called the vertex angle
- Rotating the generator 360° around the vertex and tracing out the rotation into a 3D surface gives a cone
Double right circular cone = a cone whose bases (the top and bottom faces of the cone) are perpendicular to the vertical axis and form a perfect circle
- Directrix = 2D outline of the base
- The directrix of a right circular cone is always a perfect circle
- Nappe = lateral surface of a single circular cone
- For the diagram above,
- The upper nappe is outlined in pink
- The lower nappe is outlined in blue
- For the diagram above,
Overview of Conic Sections
A conic section is the 2D curve corresponing to a particular 2D “slice” of a 3D cone
- The angle at which the 2D plane slices the 3D cone determines the type of conic section we get
Parabolas
General equation:
Circles
General equation:
- The center of the circle is defined as
- The radius of the cirlce is defined as
Ellipses
General equation:
Hyperbolas
General equation:
Sources:
- https://www.youtube.com/watch?v=PLrgwD9TleU
- https://www.youtube.com/watch?v=HO2zAU3Eppo
- Glendinning, P. (2013). Math in minutes. New York, NY: Quercus.
It looks good, but you may provide more details. For example something like driving into a conversation that helps see things better.
This is just a suggestion, which you may like 🙂 .
You may like to see my website https://scoutmathematics.wordpress.com/
Thanks! 😀 I definitely will try to add some context to my posts. Right now I’m still in blog “throw up” mode, but hopefully things will start to have more structure as I progress making the website. I’ll make sure to check out your site at some point today 😀
Thank you and also let me know how you like it (by comments there or otherwise) 🙂 .
I’m so glad I went through your site, because it looks like there is some really good stuff there. I really like your layout also. Would you mind telling me what plugin you use for your math equations?
I am not using any plugin. It is just LaTeX.
Here I can briefly tell you about using LaTeX (if you want to know more you can ask me by email : guharoyagraditya@gmail.com is my email id)
first put a $ symbol then write latex then type the line of equation, and then put the closing $ symbol.
It’s that simple.
I think you already used a little LaTeX on your website.
Actually there are some themes on wordpress that makes mathematical equations look really messy. But some themes do not make the stuff look that bad.
And I am really happy that you found my website interesting.
Soon we are planning to start a problem of the week concept, where we will be taking a problem from the submissions we receive (everyone is welcome to send us mathematical problems) put it up for about one week (sometimes this time can change), and then discuss publicly the solution and some thoughts about the problem at the end of the week and put up another problem.
Soon I’ll make an announcement of that in the website.
Hope you find that interesting too 🙂 .