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Finished Unit 1, Performing Transformation, in High School Geometry on
Khan Academy. There are a few kinds of transformations: translation,
rotate, reflection, and dilation. The first three are rigid
transformations, but dilation is not. Dilation changes the size of a
shape by scaling up or down. Rigid transformations only change a shape's
position while preserving the lengths of all lines and angles.
Translation moves an object up or down, left or right.
Rotation has a center of rotation and an angle that determines how many
degress the object moves. Positive angles rotate the object
counterclockwise, while negative angles rotate it clockwise. If the
origin is the center of rotation and the angle is a multiple of 90°, we
have some useful patterns:
R(0,0),90°(x,y) = (-y,x)
R(0,0),180°(x,y) = (-x,-y)
R(0,0),-90°(x,y) = (y,-x)
Each additional 90° counterclockwise rotation swaps the coordinates and
negates the new x-coordinate. Clockwise rotation does the same, but
negates the new y-coordinate instead. In this case, we can determine the
new position algebraically. Visualization is also useful. We can imagine
a virtual triangle or rectangle with the point as one of its vertices,
which helps us understand the rotation more intuitively.
Reflection has a line of reflection that creates a mirror image of the
original object. Every point or vertex has the same perpendicular
distance to the reflection line, extending to the opposite side by the
same distance.
I haven't started Unit 2 yet, but it seems to go deeper into the
transformations I've learned today, and there is a proof lesson at the
end of the unit. Let me tackle it tomorrow.
Besides mathematics, I am going to build a Certbot plugin for Alibaba
Cloud DNS. One of my clients has a project running on Alibaba Cloud, and
their domain names are also hosted there. Even though there are many
third-party ACME-compatible clients available that natively support
Alibaba Cloud, Certbot is still my first choice because of its
reputation and supply-chain safety. Alibaba Cloud does not have official
DNS-challenge support for Certbot, so it would be useful to have a
plugin that allows SSL certificates to be issued automatically.
A year ago I read the complete ACME protocol—RFC 8555—and implemented a
full SSL certificate issurance and renewal module in PHP, so I should be
fairly familliar with the workflow. The plugin focuses on manging DNS
records so the domain names can pass verification by the ACME server.
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EP-212 文革60周年丨严歌苓、查建英：文革就是中国人的大屠杀
https://bumingbai.net/2026/05/16/ep-212-wenge01/
I've been listening to the show through Apple Podcasts and didn't even
know it had a video version. It's a heavy topic for Chinese people, and
the two guests shared the tragic stories from their youth. It's hard to
image how people survived those difficult times, when violence and
irrationality shaped everyone's life.
---
What I've learned about learning a language
https://petargyurov.com/2022-10-30/learning-spanish
I discovered this blog through Hacker News today, although not because
of this article specifically. I've also noticed that compared to my
English reading and writing skills, my speaking and listening are much
weaker.
Watching YouTube videos and listening to podcasts are my favorite ways
to improve my listening, but sometimes the episodes are hard to follow,
and finding material that suits my current level is not easy.
I've tried improving my speaking with ChatGPT serveral times before, and
I liked the experience. One great advantage is that it never gets
frustrated and always has the patience to listen to me. All I need is a
topic to talk about. Maybe the next time I run into a problem in daily
life, I should talk to it instead of typing on the keyboard.
I also like Duolingo, but the streak system really annoys me. I don't
need it to feel that I am making progress, and the streaks sometimes put
pressure on me. I don't think missing a day or two really matters, and
I wish there were an option to turn it off.
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