Darth Calculus 🏳️‍🌈

I don't like dealing with significant digits or rounding in non-decimal number systems. But they exist and we should be able to deal with them

Sounds like a good one-day enrichment activity or an asynchronous remote activity. I convert between radians/sec, deg/sec and RPM in physics. It's a good side-skill

That show!!! So nostalgic.

"Wrathful ones nine eyes gaze
Holding skulls
Filled and laced
With human blood"

Mastodon - Ghost of Karelia

My favorite footprint phenomenon has happened again! This time more impressively because of the depth of the snow. Reminds me of differential weathering in monument valley

Every time I drive by a field full of geese the Jurassic Park theme plays in my head

🚫 can't
🛶 Oar
🌅 Set

Cantor set!

🚫🛶🌅

I don't know which of these is better, so that's actually a hint:
🐓❄️ or 🥤❄️

Oh, that's why I didn't recognize them! I don't know those terms

That is absolutely fascinating! Never came up when I was in college. I have to remember that even the "real" equation may just be a better approximation

A screenshot of a Desmos graph that shows how a ray of light refracts and reflects within a water droplet to produce a rainbow

A screenshot of a desmos simulation that shows the path of a ray of light refracting through and reflecting off the back of a water droplet. Normal lines and angles are shown.

I had a productive day in #Desmos today. I also made a simulation of the refraction and internal reflection that causes rainbows. Enjoy, #EduSky and #MathSky ! #IteachPhysics

Full spectrum: www.desmos.com/geometry/hga...
(reverse contrast!)

Single ray with angles: www.desmos.com/geometry/l32...

A sign commemorating Frederick Douglass

I had Frederick Douglass on my mind because yesterday was his chosen birthday, but I didn't know I'd be in this area today

#EduSky If you like geometrical optics, you might also like this simulation of refraction through a spherical lens I made in #Desmos. The adjustable ray is parallel to the optical axis. You can also change the sphere's radius.

www.desmos.com/geometry/tjl...

Prism Refraction (Spectrum)

I cleaned up the interface on the one with the spectrum. I didn't realize I could put angles inside of folders to deactivate them!

www.desmos.com/geometry/vp0...

Drop an album that was important to you when you were 19.

Screenshot of single-ray refraction simulator in desmos. It shows incident and refracted angles for both internal and external rays through an equilateral triangular prism.

Screenshot of multiple-ray refraction simulator in desmos. Each ray is color-coded to match the refractive index for that wavelength. It shows incident and refracted angles for both internal and external rays through an equilateral triangular prism

A close-up of the different refracted rays of light through a prism in a desmos simulation

I made a simulation of refraction through a prism in #Desmos this morning. The incident beam and corners of the prism are adjustable. Give it a shot, #EduSky !

Single ray: www.desmos.com/geometry/skt...

Spectrum: www.desmos.com/geometry/s6x...
(reverse contrast!)

Has there already been a "loss" cow tools?

Best example that was ever set for me - when I was an underclassmen in college, an influential senior apologized the next day after missing a meeting. We all would have let it slide but he stopped and acknowledged it. I have never forgotten that simple act of humility and respect.

Not watching the Superbowl today, but I wanted to mention...I had never listened to Bad Bunny. I assumed it was pop drivel that only kids liked. Boy, was I wrong! I listened to a few songs and it brought me back to my college jazz band days. Anything with real horn arrangements is ok with me 🎺

I need to read this every morning

I can rationalize the difference between the natural numbers and whole numbers, but I would have made them one category if I was making it all up

Every time I think I'm being righteous I realize I'm being self-righteous

I think "rising to the occasion" is the "manly" thing to do, and you did it. 🤝 Some men want to pick the occasions, but we don't get to.

I sat stunned for a while and had a conversation with my kids who I had mostly kept protected.

It's what breaks us out of our complacent certainty to begin a real investigation. I would have soothed my doubts with apologetics if the fruit of the spirit were evident as they should be

I'm sure they were "just following orders"

My bad, that's Lösch. I have never heard of these numbers before today...do they have some interesting application?

An unsuccessful attempt to prove that L is closed under multiplication

I'll have to quit here. I thought I could express the product of two Löschian numbers as another Löschian number:
(a² + ab + b²)(c² + cd + d²) = (x² + xy + y²)

But I couldn't figure out a way to express x and y in terms of a, b, c, and d.

I am so upset that it's ab instead of 2ab. That Löschian was a madman

At first, I was concerned for my physics curriculum. Then I read more carefully