Ptolemies

Star Cluster M7

Messier 7 (also known as NGC 6475) is an open cluster of stars in the constellation of Scorpius and the southern most object in the Messier Catalog. The Cluster is sometime referred to as the Ptolemy Cluster because it was first observed by the Greek Astronomer Ptolemy in 130 AD. The cluster is easily viewable with the naked eye, close to the tail’s stinger of Scorpius. This particular image was taken at ESO’s La Silla Observatory in Chile.

Credit: ESO / La Silla

We have three colored segment in this animation. Surprisingly the length of the longest one is always the sum of the length of the two smaller ones.

This is actually a very special case of Ptolemy’s theorem. The theorem gives a connection between the sides and the diagonals of a cyclic quadrilateral. In this case the length of the dashed lines is equal so the theorem can be simplified to the statement above. 

6

“You are now rocking with the very best
Rapper from around the way
I wanna say hello! (hello!)
Everybody calls me by my old name
So lame, you can just call me “Pharaoh”
Ain’t nobody stoppin’ this
Pharaoh's on top of this
Too many things in the day to try to fit in
All of you should stand up ‘nd dance, no sittin’
Straight up out the tomb big dreams on my mind
Gotta find my way in this Boo York way of life”

x

I don’t want to be a god,” I said. “You don’t get that, do you? You couldn’t find anything about me you could relate to, which I take as a big compliment.
— 

Percy Jackson, Crown of Ptolemy (Rick Riordan)


This part just gets to me every time I read it because I flash back to the time Percy was offered immortality, and I thought about the reasons he did so. 

Sure, Percy has been through hell and back, but he would never give his mortality away – even if it is for something like being a god. He would never give his shot at his life away. He would never give Annabeth away.

And I believe that in itself is just so freaking beautiful.

As for Sadie, she didn’t appear interested in strategy. She leaped from puddle to puddle in her combat boots. She hummed to herself, twirled like a little kid and occasionally pulled random things out of her backpack: wax animal figurines, some string, a piece of chalk, a bright yellow bag of candy.
She reminded me of someone …
Then it occurred to me. She looked like a younger version of Annabeth, but her fidgeting and hyperness reminded me of … well, me. If Annabeth and I ever had a daughter, she might be a lot like Sadie.
Whoa.
It’s not like I’d never dreamed about kids before. I mean, you date someone for over a year, the idea is going to be in the back of your mind somewhere, right? But still – I’m barely seventeen. I’m not ready to think too seriously about stuff like that. Also, I’m a demigod. On a day-to-day basis, I’m busy just trying to stay alive.
Yet, looking at Sadie, I could imagine that someday maybe I’d have a little girl who looked like Annabeth and acted like me – a cute little hellion of a demigod, stomping through puddles and flattening monsters with magic camels.
I must have been staring, because Sadie frowned at me. ‘What?’
‘Nothing,’ I said quickly.
— 

The Crown of Ptolemy by Rick Riordan

I swear if this doesn’t make you smile and squeal you can’t talk to me

7

The Harmonia Macrocosmica of Andreas Cellarius

3.ORBIUM PLANETARUM TERRAM COMPLECTENTIUM SCENOGRAPHIA - Scenography of the planetary orbits encompassing the Earth.    

5.SCENOGRAPHIA SYSTEMATIS COPERNICANI - Scenography of the Copernican world system.   

10.CORPORUM COELESTIUM MAGNITUDINES - The sizes of the celestial bodies [in some copies the terrestrial sphere has the continents drawn in by hand].   

15. TYPUS ASPECTUUM, OPPOSITIONUM ET CONIUNCTIONUM ETZ IN PLANETIS - The (astrological) aspects, such as opposition, conjunction, etc., among the planets.    

16. THEORIA SOLIS PER ECCENTRICUM SINE EPICYCLO - Representation of the Sun in an eccentric orbit without epicycles.    

18. THEORIA LUNÆ, EIUS MOTUM PER ECCENTRICVM ET EPICYCLVM DEMONSTRANS - Representation of the Moon showing its motion in an eccentric orbit with epicycles.    

19. TYPUS SELENOGRAPHICUS LUNÆ PHASES ET ASPECTUS VARIOS ADUMBRANS [some copies from the 1660 edition have the nonsensical reading ‘… OS ADVARIUMBRANS’] - Selenographic diagram depicting the varying phases and appearances of the Moon by (means of) shading.

source: Theological Institute, University of Utrecht

She looked like a younger version of Annabeth, but her fidgeting and hyperness reminded me of….well, me. If Annabeth and I ever had a daughter, she might be a lot like Sadie.

Whoa.
It’s not like I’d never dreamed about kids before. I mean, you date someone for over a year, the idea is gong to be in the back of your mind somewhere, right? But still- I’m not ready to think too seriously about stuff like that. Also, I’m a demigod. On a day-to-day basis, I’m busy just trying to stay alive.

Yet, looking at Sadie, I could imagine that someday maybe I’d have a little girl who looked like Annabeth and acted like me-a cute hellion of a demigod, stomping through puddles and flattening monsters with magic camels.

—  Percy Jackson about Sadie Kane, the Crown of Ptolemy by Rick Riordan.