From ancient civilizations to modern mathematics: the evolution of the magic square qzz

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A magic square is a square grid of numbers where the sum of the numbers in each row, column, and diagonal is the same. This sum is known as the magic constant. Each number in the grid is unique and typically starts from 1 and goes up to n^2, where n is the size of the grid. In order to create a magic square, there are various methods and algorithms. One popular method is the Siamese method, which involves filling in the numbers diagonally in a specific pattern. Another method is the odd-ordered method, which works best for grids of odd dimensions.


About four miles in, still along the ridge, a pair of white-haired hikers appeared up ahead, walking towards me. When I pulled aside to let them pass, they warned me that a rattlesnake was stretched out across the trail about 100 feet ahead. We chatted about rattlesnakes and Arizona for a minute or two and then went our separate ways.

When I reached Jennings Creek Road, I left the AT and headed up VA614 toward the Middle Creek Campground where Kate had secured a campsite for the night. To say that Chad Sell s first graphic novel, The Cardboard Kingdom , co-written as part of a team of ten comics collaborators and starring a group of neighbor kids who bond together one summer over their imagined alter egos, was a massive hit with my kids three years ago would be a gross understatement.

The sky blue nosed witch

Another method is the odd-ordered method, which works best for grids of odd dimensions. Magic squares have fascinated mathematicians and puzzle enthusiasts for many centuries. They have been found in ancient civilizations and are even mentioned in ancient Sanskrit texts.

Day 58: An Angel, a Serpent, an Attack Fawn, a Witch, Caesar, and Blue Blazin’

I woke up feeling off, but not quite sick. I wasn’t hungry, which was weird, and I couldn’t finish my oatmeal. Oatmeal never goes unfinished at my breakfast table. And my stomach still had that bloated about-to-explode feeling. Clearly, the best thing to do was strap on a tight hip belt and go hiking.

Hiking downhill, of course, and only eight miles. Though when I started out, I realized I’d misread the mileage and had thought I only had six. Six, eight, twenty-one, it’s all the same thing. I just wanted to chip something off the distance to Katahdin. Plus, we’d cleaned all the ticks off Gus, and he was ready to hunt down a fresh batch.

The Hike

I couldn’t have asked for a nicer day. The woods smelled great this morning – a hint of pine, but basically just refreshing, clean air. I don’t think I’ve ever noticed it before.

After a short climb out of Bear Wallow Gap, the trail gradually descended to Jennings and Middle Creeks. Perfect for walking, seeing, and seeing what I see.

And thinking. I spent the morning in my head thinking about my adolescence and the trials I put my poor parents through. I have no idea why my brain went there. It’s probably the same answer I gave guy on Facebook who asked how in the world did I think of dividing the AT’s length by Pi to come up with the 700-mile Pi(e) Challenge. I answered him, “Dude, I’ve been hiking alone for 58 days. There’s nothing I haven’t thought about.”

Providence or Serendipity?

About four miles in, still along the ridge, a pair of white-haired hikers appeared up ahead, walking towards me. When I pulled aside to let them pass, they warned me that a rattlesnake was stretched out across the trail about 100 feet ahead. We chatted about rattlesnakes and Arizona for a minute or two and then went our separate ways.

After they hiked on, I thought how fortunate to have met them just then, as I had been distracted and inattentive all morning. I could have easily stepped right on the snake without noticing.

I walked up slowly and found a three- to four-foot rattler, with his head in a bush and his tail halfway across the trail. Given his girth, he’d just eaten something. Thinking he’d be fat and happy, I tried to sneak by, but he was in no mood to share the trail. He coiled up, stuck his buzzer straight up, and put his head in the attack position. Gus and I backed up and found an alternate route through the brush.

If the Snake Doesn’t Get You, the Fawn Will

After passing Mr. Buzzworm, I pulled out my camera to record a video about him. When I did, I saw a doe and fawn standing in the trail about 150 feet ahead. I switched to camera mode and tried to zoom in, expecting them to bound off before I could focus. Instead, they walked right toward us.

Great, I thought, I survived the rattlesnake but am going to be killed by a rabid fawn. Actually, I’m pretty sure the doe saw Gus and assumed I had a little brown fawn of my own. She was bringing hers over for a play date. When they got to within 15 feet, Gus decided a play date would be just fine and walked over to meet them. Frankly, he was so quiet, I’d forgotten he was behind me and off leash.

Once Gus came out from behind me, the doe realized that my fawn was too ugly to play with hers and jumped to the left. The fawn jumped right. Gus spun in place trying to keep both of them in front of him. And then it got a little chaotic. The fawn ran off and doe started running circles around Gus, darting back and forth across the trail, all while doing this weird hacking cough thing. For his part, Gus never barked or chased either of them, and he came right back when I called him.

As Gus came back, the doe ran around behind me, passing a few feet away and cough/hacked her way through the underbrush over the ridge where the fawn had gone. Bizarre. I’d never seen anything like it.

Did Anyone Else See All That?

Five minutes later I saw a backpacker ahead of me. She was all bundled up like it was cold out. Her hood was up, covering her face, and she wore gloves and long pants. I greeted her, but she was grumpy and sullen. I was still pumped with adrenaline, so I asked if she saw the rattlesnake.

“Snake?” she said. Now she was interested. The hood came off to reveal raven-black hair. And was that a wart on her hooked nose? “Where?” she asked eagerly.

“Well,” I said, “Did you pass an older couple a few minutes ago on the ridge?” She gave me a weird look and said she hadn’t seen anyone all day. What? How could you not see two friendly people walk right past you? She shrugged and suddenly lost interest.

The Only Rational Explanation

Then it dawned on me. Clearly, the older couple were guardian angels sent to warn me of impending danger in the form of an evil serpent. Obviously, the grumpy woman was a snake-loving witch unable to see angels. Or she had left the snake on the trail to get me, possibly her revenge for noticing the cryptids along Dismal Creek last week.

I’m not sure how the fawn fits into all that. Maybe it’s the exception that proves the rule, or maybe it was an evil fawn infected with deer ticks. Or more likely, that I should have stayed in bed another day.

What About Caesar?

I did promise a Caesar, didn’t I? Eight miles counts as a nero, right? And Nero was one of the … Never mind, blame it on the fever.

Blue Blazin’

When I reached Jennings Creek Road, I left the AT and headed up VA614 toward the Middle Creek Campground where Kate had secured a campsite for the night. That’s right, I blue blazed* 1.5 miles. In the morning, I’ll blue blaze right out again, connecting back up with the AT a few miles north.

No apologies, no rationale, no guilt. I’m hiking my own hike, which we now know has been blessed by angels.

Daily Stats:

  • Start: Bearwallow Gap (Mile 751.9)
  • End: Middle Creek Campground (Mile 760.0)
  • Weather: Slightly overcast, cool.
  • Earworm: Witchy Woman (Eagles)
  • Meditation: Mt. 6:34
  • Plant of the Day: Jersey Tea
  • Best Thing: Fawn
  • Worst Thing: Rattlesnake

*Blue blazing is leaving the main trail for an alternative or side trail, and is frowned on by stuffy, so-called “purists.”

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Magic square qzz

The properties and patterns of magic squares have been studied extensively, and they have many interesting mathematical properties. Magic squares are not only limited to numbers. They can also be created using symbols, letters, or even colors. In these cases, the objective is to arrange the symbols in a square grid such that the sum of the symbols in each row, column, and diagonal remains the same. Magic squares have also found practical applications in cryptography, game theory, and even in creating puzzles and brain teasers. They provide a challenge for problem-solving and can be a fun way to exercise the mind. In conclusion, magic squares are fascinating mathematical objects that have been studied and admired for centuries. They have unique properties and can be created using various methods and even with different symbols. Whether used for practical applications or as a source of entertainment, magic squares continue to captivate the minds of mathematicians and enthusiasts alike..

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