#XZ3

[postsofbabel]

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[jzlily333]

🌺08/21LiveWell活出美好🌺

Forgiveness is the only key to deliverance and freedom from bitterness.                       

Forgive, and you will be forgiven (forgiveness: original text means release);… (Luke 6:37).

08/21 Bible verses

My son, let not them depart from thin eyes: keep sound wisdom and discretion. (Proverbs 3: 21)

My son, guard true wisdom and counsel, and do not let it depart from your eyes (Proverbs 3:21).

08/21Good words of wisdom

1. Calm down and appreciate yourself, your endurance, courage and confidence, and then taste the sweetness contained in life.

2. Once a person has self-awareness , there will be very helpful to overcome difficulties in life. 

Hymn: Please fill me with the Lord

https://youtu.be/xZ3-_Tx0Kfg?si=QAiMDvE8b8aJGxXc

🌺08/21活出美好🌺

寬恕是唯一能讓你從苦毒中被釋放、得自由的關鍵。         

你們要饒恕人，就必蒙饒恕(饒恕:原文作釋放)；… (路加6: 37)。

08/21圣经金句

My son, let not them depart from thine eyes: keep sound wisdom and discretion.  (Proverbs 3: 21)          

我兒，要謹守真智慧和謀略，不可使他離開你的眼目(箴言3: 21)。

08/21金玉良言

1. 靜下心來欣賞自己，欣賞自己的耐力、勇氣與信心，進而用心品嚐苦澀的生活中所蘊含的甜美滋味。

2. 人一旦有了自知之明，也就沒有什麼克服不了的困難，沒有什麼過不去的難關。

詩歌：求主充滿我 

https://youtu.be/xZ3-_Tx0Kfg?si=QAiMDvE8b8aJGxXc

[thebrilliot]

Rubik's cube solving agent: Rotation

The very first decisions I had to make about coding a Rubik's cube were about how to represent them. They are a subgroup of S48 but I really did not want to code the movement of facelets 20 at a time, 18 times. So I went and researched how a whole cube or a single cubelet could be represented by its orientation.

The group of a cube's orientation or rotation is isomorphic with the S4 group which has 24 elements under composition. I tried reading about how they are represented and it looks like there are two different notations for rotations. You can use extrinsic or intrinsic axes and I don't know which is which, but after failing to understand how to do it, I made my own notation. The most common notation is x-z'-x" so I'll call mine xy-xz notation.

xy-xz Notation

Here's my rationale for this notation. You can construct the group of cube rotations with just 2 elements: the X rotation and the Z rotation which, I assume, is where the x-z'-x" notation comes from. You only need two axes. My problem is that, apparently, three separate steps is too much for my brain and I would rather add the y-axis so I can take shortcuts, and anyway I don't know if I'm supposed to use intrinsic or extrinsic axes.

So I like to keep the axes in place and not rotate them with the cube (someone else can figure out if that's intrinsic or extrinsic), and instead of using X and Z, I use X, Y, and Z. You only ever need two constructors to get where you need and there are always 3 (or maybe 6?) ways to write the rotation this way. So in the event you need two constructors, always put X first. Writing the rotations this way gives us the following: e (neutral), X, X2, X3, Y, Y2, Y3, Z, Z2, Z3, XY, XY2, XY3, XZ, XZ2, XZ3, X2Y, X2Y3, X2Z, X2Z3, X3Y, X3Y3, X3Z, and X3Z3. X2Y2, X2Z2, X3Y2, and X3Z2 reduce to Z2, Y2, XZ2, and XY2, respectively.

Clockwise and Counterclockwise

I also had to decide what counted as clockwise and counterclockwise which would get confusing very quickly because cubes are perfectly symmetrical. I decided consistency is key. Imagine a cube floating in a 3D Cartesian space if you will. Most people are comfortable viewing things from an isometric viewpoint. But the isometric viewpoint looks does not look at the sides of this cube from the same direction on each axis. You are looking from the negative Y direction and the positive X and Z directions. I thought, this is group theory; it's technically math. Let's do something that is mathematically sane. Let's set clockwise based on the positive and negative directions of each axis. So looking from the negative side of each axis, draw clockwise on the nearest three faces of the cube. I know it's a bit of a stretch but you're looking at the front and left of the cube from below. The other solution was to look from the positive side of each axis, i.e. at the top and right of the cube from the back which is equally messed up. And now we can officially define the X, Y, and Z rotations as 1 quarter-turn around their respective axes.

Why?

I know that was all very pedantic but it was necessary. First, because it will make the code much easier because of ✨consistency✨. Second, because I don't have any mathematician friends and I'm making this up as I go.

Now we don't have to keep track of 48 facelets and make sure they are always synced with each other. We only have to keep track of 20 cubelets and their orientations. Note that we discover an interesting relationship between cubelet positions and orientations. As cubelets rotate, they change position. However, there are more rotations than there are positions. Edge cubelets have 12 possible positions and corner cubelets have 8 possible positions. This means that every edge position has 2 possible rotations per cubelet and every corner position has 3 possible rotations per cubelet. Meaning if we know the rotation of a cubelet (for example, the blue-red-white cubelet), then we also know its position which is extremely convenient. Conversely, given a cubelet's position and rotation, we know which cubelet it is. This means we can represent a cube with an array of just 20 bytes, one byte for the rotation of each cubelet, without losing any information.

P.S. I have no idea if I posted this already but here it is

[yenicagkibris]

Beş dakikada değişir bu demokrasi işleri - Gözde Bedeloğlu

[rizkacreations]

Give your Sony Xperia XZ3 a makeover with our Clear/Gloss Hydrogel Screen Protector & 3D Printed Backskin. Flaunt a glossy finish and shield your screen from scratches, maintaining a pristine look. | rizkaCreations.com

.

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#xz3 #sonyxperia #xperia #sonyxperiaxz3 #xperiaxz3 #rizkaCreations #hydrogelscreenprotector #hydrogel

[mikkisworld]

Check out this listing I just added to my Poshmark closet: ♠️ KATE SPADE "HELLO" THEMED AQUA CHARGING TRAY.

[rohailk94]

Loving Xperia XZ3's camera #ginger #photography #sony #xz3 #smartphonephotography #vegetablephotography (at Punjab, Pakistan) https://www.instagram.com/p/B8mX-jrJj6S/?igshid=12nqrqm3adyjc

[zodiac208]

Stickers on the back of the screen Sony XZ 1, XZ2, XZ3, XZ premium

See details: https://pskin.vn/dan-mat-lung-man-hinh-sony-xperia-xz-ppf-4d-da-skin-tot-nhat/

[avozdepetropolis]

Independent Strategy Analytics mostra que o Sony Xperia XZ3 tem o melhor ecrã

Independent Strategy Analytics mostra que o Sony Xperia XZ3 tem o melhor ecrã

[ad_1]

A Sony teve um dos seus equipamentos testado pela Strategy Analytics. A empresa foi incumbida de realizar um teste independente ao ecrã do Xperia XZ3. Essa é o novo ecrã P-OLED com resolução de 1.440 x 2.880px.

Para a competição, s SAreuniu o que considerou os principais telefones no mercado. Aqui está a lista abaixo. Observem que o teste foi feito entre 21 e 23 de agosto, então o…

[postsofbabel]

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[jzlily333]

🌺06/12LiveWell活出美好🌺

May God’s love fill us and allow us to become angels spreading love, unity, tolerance and forgiveness.​​

There is a peacemaker! For they will be called sons of God (Matthew 5:9).

06/12 Bible verses

For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe. (1 Corinthians 1: 21)

The world through its own wisdom did not know God, but God was pleased through the foolishness of man’s teaching to save those who believe. This is the wisdom of God (1 Corinthians 1:21).

06/12Good words of wisdom

1. When misfortune strikes, don’t be discouraged, depressed, or decadent. Because misfortune is temporary and ups and downs are inevitable. When encountering sudden setbacks and misfortunes, it’s time to turn!

2. When you encounter obstacles on the road of life, learn to turn around at the right time! I believe that life will be full of twists and turns, and the road ahead will not always be bumpy.

Hymn: Please fill me with the Lord

https://youtu.be/xZ3-_Tx0Kfg?si=QAiMDvE8b8aJGxXc

🌺06/12活出美好🌺

願上帝的愛充滿我們，讓我們成為散播愛、合一、寬容、饒恕的天使。    

使人和睦的人有了！因為他們必稱為神的兒子(馬太褔音5: 9)。

06/12圣经金句

For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe. (1 Corinthians 1: 21)      

世人憑自己的智慧，既不認識神， 神就樂意用人所當作愚拙的道理，拯救那些信的人。這就是 神的智慧了 (哥林多前書1: 21)。

06/12金玉良言

1. 當不幸降臨的時候，不要氣餒，不要消沈，不要頹廢 。因為不幸是暫時的，坎坷是難免的。遭遇突發的坎坷和不幸，就是「 該轉彎了！」

2. 在人生路上遇到障礙物的時候，適時地學會拐個彎吧！相信人生會峰迴路轉，柳暗花明，前面的路一定會���暢的 。  

詩歌：求主充滿我 

https://youtu.be/xZ3-_Tx0Kfg?si=QAiMDvE8b8aJGxXc

[rajeshmevliya]

#sony #xperia #xperiaxz3 #xz3 #xz2premium #xz2 #xperiaxz2 #xz2compact #xz #xperiaxz #xzpremium #xzs #xperiaxzs #playstation #playstation4 #playstation2 #playstation3 #playstation #sonywh1000xm3 #xz4 #XZ4 #xperiaxz4 #mkbhd #xperia1 #xperia10 #xperia10plus #xperia10ii #xperia1ii #sonyxperia1mark2 #allabouttech00 #digitalbaazaar https://www.instagram.com/p/CBW7eZpAPiD/?igshid=8ux84xyicnnv

[androidnews-blog]

#sony #xperia #xperiaxz3 #xz3 #xz2premium #xz2 #xperiaxz2 #xz2compact #xz #xperiaxz #xzpremium #xzs #xperiaxzs #playstation #playstation4 #playstation2 #playstation3 #playstation #sonywh1000xm3 #xz4 #xperiaxz4 #mkbhd #xperia1 #xperia10 #xperia10plus #xperiac #sonyxperia #xperia10ii #xperia1ii #sonyxperia1mark2 https://www.instagram.com/p/CAamebsjSSH/?igshid=a98x4pzdgwr1

[convxction]

[[in every game/world/verse chrom gets send to another realm, his only mission is always to train ppl ... why are you so obsessed with training, dude? d/ragalia lost--training the ‘army’. p/roject x zone--he is picking fights with everyone in the training room XD. even in warriors and heroes ... this man can’t be stopped. waiting for more cameos to see who else he is going to bother lmao.

[rohailk94]

I was on my way to the market when I saw a lonely leaf just lying on the floor. As a nature lover how can I resist it. I was with my family so didn't have much time but still convinced them to stop and took these beautiful pattern of nature. #pakistanphotographyhub #iger_pakistan #xz3 #Xperia #PHOTOGRAPHY #naturephotography #patternphotography (at Lahore, Pakistan) https://www.instagram.com/p/B9bpKPlgtDA/?igshid=1809lj1c6xvmc

[kazukijamesfinch]

My old phone case (that I used for 3 years I think)....yuk.

My new case arrived today.

Kinda a dumb post just wanted show the state of my old knackered case.