Harof and Lynn pulled the thin rope taut together, one end pressed under the ice column, while the other end overlapped with the shadow.
When the magical clock struck exactly twelve o'clock, Harof used his hand like a blade and precisely cut the remaining rope.
"Ruler, hurry, pass me the ruler." Harof shouted excitedly, so hurried in his descent that he forgot the most crucial tool.
Elok, with quick reflexes, immediately ran back to the airship and handed the ruler to Harof within ten seconds.
The legendary wizard took the ruler with great solemnity, as if on a pilgrimage, and began to measure the length in segments.
"Harof, what's the length of the shadow?" several accompanying wizards asked with great anticipation.
Harof didn't answer immediately but measured multiple times before speaking cautiously. "It's 1,051 centimeters, or 10.51 meters."
With the data in hand, everyone quickly took out a pen and paper to calculate. The wizards, who hadn't formally studied advanced mathematics, still knew basic geometry.
However, this value wasn't a whole number. With decimals, squaring and taking the square root doubled the calculation complexity. It took over five minutes for them to calculate that the length of the hypotenuse was approximately 100.55 meters.
After over two months of mathematical training, Lydia and Elok were clearly quicker than the rest. They had already started calculating the angles of the triangle, using trigonometric formulas to determine the sine of the opposite side over the hypotenuse.
"I've calculated it. The angle is six degrees." Lydia, the first to calculate it, waved her arms vigorously and shouted loudly.
Harof, who didn't have pen and paper, also arrived at the answer through mental calculation at the same time. Lydia's calculation was correct; the triangle's apex angle and the corresponding angle on the Earth were indeed six degrees.
The rest was straightforward. A circle had 360 degrees, so the Earth's angle meant dividing the entire circle into sixty equal parts, each being 720 kilometers. So, the total length was...
"43,200 kilometers." Harof's voice trembled, and he repeated the calculation several times in his mind, afraid of making a mistake. After confirming it was correct, he said, almost in a dream, "43,200 kilometers. This is the circumference of our planet."
Lynn, of course, was the fastest to calculate. After receiving the shadow length data from the AI in his brain, he instantly had the answer.
It seemed that this alien planet was slightly larger than Earth in his previous life.
If he remembered correctly, Earth's circumference was around 40,075 kilometers, and the two values were quite close.
The other wizards quickly calculated the same value, and they were all thrilled. Once they knew the circumference, calculating the diameter, radius, and surface area was only a matter of time.
On the side, Rol didn't participate in the calculations. Instead, he created another new painting, titled [People Measuring the Planet's Circumference Under the Blazing Sun and Ice.] His ink-dipped quill danced rapidly on parchment.
Harof, using the ruler to measure the rope's length, Lynn estimating the central angle, Lydia jumping with excitement, and the wizards in the background deep in thought all vividly appeared on paper. Against the backdrop of the harsh sun and floating ice islands, the scene was bizarre yet harmonious, forming a striking and beautiful picture.
After pouring his inspiration onto the canvas, Rol looked at the two paintings in his hand and felt that his life was now complete. He was well aware that these two pieces would be remembered by people for generations to come during this historic moment.
However, after composing himself, Rol didn't forget about another crucial matter, as some people couldn't wait any longer.
Thinking of this, Rol turned to Harof and asked, "Harof, should we send this message to Greenville now?"
Harof, who was calculating the planet's surface area, didn't have time to respond but simply nodded. "Now that we've confirmed it, send it."
Meanwhile, in the city of Greenville, a dozen alchemists were anxiously waiting by the communication alchemical array, hoping for news from the other side.
But it was already 12:37, and they hadn't received any messages, making Raphael and the others begin to doubt if the operation had failed. Could it be that Lynn's assumption was incorrect, and this continent wasn't spherical after all?
"Look, there's movement." A sharp-eyed alchemist was the first to notice the alchemical array glowing. Everyone rushed over.
Since the distance was over 700 kilometers, the amount of mana required for transmission was a staggering number, so Rol had only sent the two most crucial pieces of data: the shadow length and the apex angle.
"The shadow length is 10.51 meters, and the apex angle is 6 degrees..." Raphael, watching the data formed by magical energy inside the alchemical array, shouted excitedly.
Thanks to a sound-amplifying spell, this message quickly spread throughout Greenville City. The entire city of wizards seemed to be in a frenzy as countless wizards, who had eagerly anticipated this moment, took out parchment and quills to start their calculations. Even some educated civilians joined in.
Calculating the data with just the shadow length required a solid understanding of trigonometric functions, which was enough to baffle most wizards. However, once they had the apex angle, it became basic multiplication and division, something even some commoners could handle.
"The planet's circumference is 43,200 kilometers, the diameter is approximately 17,751 kilometers, and the surface area is 594 million square kilometers?" On the crowded streets of Greenville City, Yal observed the just-calculated data, murmuring to himself.
He wasn't a wizard, or perhaps he lacked the aptitude, and never had the chance to become a wizard's apprentice. But, driven by a deep interest in mathematics, he had once thought that his math skills would only be useful for everyday transactions and, at best, make him a tax collector. However, the last issue of the "Magic Daily" opened a new world for him.
A wizard named Lynn, who had come from beyond the Misty Sea, was planning to measure the circumference of their planet using just a few simple mathematical formulas, without the need for any magic.
Yal had doubted whether it could be that simple, but when these values were revealed on paper, all his doubts vanished. The overwhelming shock he felt couldn't be quenched, as if the world was unfolding beneath his pen.