Harrov and Lynn stretched the thin rope taut, anchoring one end beneath the ice pillar and overlapping the other end with the shadow.
As the magic clock struck precisely twelve o’clock, Harrov, using his hand as a blade, cut the remaining rope with great precision!
"The ruler, quick, bring the ruler!" Harrov shouted excitedly, having co down so hastily that he had actually forgotten to bring the most important tool.
Quick-witted Ailoke imdiately ran back to the airship, and in less than ten seconds, he had the ruler in Harrov’s hands.
This legendary wizard solemnly received the ruler and began to asure the lengths section by section, as if on a pilgrimage.
"Master Harrov, how long is the shadow!" A few of the accompanying wizards asked eagerly, full of anticipation.
Harrov did not answer imdiately; instead, he asured several tis before speaking in a deliberate tone. "It is one thousand and fifty-one centiters, that is, 10.51 ters!"
With the data in hand, everyone imdiately took out paper and pen to calculate. The grand wizards qualified to witness this experint aboard the airship—although not systematically educated in Olympiad mathematics—still understood the basic thods of geotric calculation.
However, this value was not an integer. With a decimal involved, squaring and then taking the square root multiplied the amount of calculation needed. It took them over five minutes to approximate the hypotenuse’s length to about 100.55 ters using the Pythagorean theorem.
Lydia and Ailoke, who had undergone more than two months of Olympiad math training, were clearly faster and had already begun calculating the angle of the vertex, substituting into the triangle formula, where sine (sin) equals opposite over hypotenuse...
"I’ve got it, the vertex angle is six degrees!" Lydia, the first to calculate the result, waved her arms vigorously and shouted loudly.
Harrov, who had not used pen and paper, also arrived at the answer through ntal calculation at the sa mont—Lydia had not made a mistake; indeed, the vertex angle and its corresponding central angle of the Earth was six degrees!
The rest was easy. A circle has three hundred sixty degrees, the Earth’s central angle was divided into sixty equal parts, each part being seven hundred twenty kiloters, so the total length would be...
"Forty-three thousand two hundred kiloters!" Harrov’s voice trembled; he had run through the calculations several tis in his mind, fearing any omissions. Only after confirming the accuracy did he speak as if in a trance, "Forty-three thousand two hundred kiloters! This is the circumference of the planet beneath our feet!"
Lynn naturally completed the calculations the fastest. His cybernetic brain directly presented the answer in his mind once it had received the data for the shadow’s length.
It appeared that this alien planet was slightly larger than Earth in his previous life.
If he rembered correctly, the circumference of the Earth should be forty thousand seventy-five kiloters, and the two numbers were very close to each other.
The rest of the wizards also quickly calculated this value, each one buzzing with unrestrained excitent. Once the circumference was known, computing the diater, radius, and area was simply a matter of ti.
To the side, Luo’er did not join the computation but instead created a new painting titled "Between Fierce Sun and Frigid Ice, the People asuring the Planet’s Circumference"!
The ink-dipped quill pen danced quickly over the parchnt.
Harrov asuring the rope with a ruler, Lynn gazing into the sky as if estimating the Earth’s central angle, Lydia leaping high in excitent, and the wizards behind them deep in thought—all sprang to life on the paper, forming a striking and harmonious scene against the backdrop of the harsh sun and Floating Ice Island.
After exhausting his inspiration, Luo’er looked at the two scrolls in his hands, feeling his life was now complete!
He was keenly aware that these paintings would forever be rembered by the world along with this historic mont!
However, after composing his emotions, Luo’er did not forget another urgent matter, lest certain individuals beco too impatient.
With this thought, Luo’er turned to Harrov and inquired, "Master Harrov, shall we send the news to Greenrill City now?"
Harrov, busy calculating the planet’s surface area, had no ti to spare, rely nodding nonchalantly. "Since it has been confird, send it!"
...
anwhile, in Greenrill City, a dozen alchemists anxiously waited before the communication Alchemy Array, eager for news from the other side.
But now it was already twelve thirty-seven, and no ssage had co through, which made Rafael and the others start to fear that the mission had failed.
Could it be that Lynn’s hypothesis was incorrect and that this continent was not spherical?
"Look, there’s sothing happening!" An eagle-eyed alchemist was the first to notice the Array lighting up; everyone imdiately crowded around it.
Due to the distance of over seven hundred kiloters, the consumption of magic stones needed for transferring information was a terrifying figure, so Luo’er only transmitted the two most crucial pieces of data: the shadow length and the vertex angle.
"The shadow is 10.51 ters long, and the vertex angle is six degrees…" Rafael, looking at the flickering data made up of magic power within the Alchemy Array, shouted excitedly.
Amplified by magic, this news quickly spread throughout Greenrill City, and an extraordinary scene unfolded. Countless eager wizards simultaneously took out parchnt and quills to start calculations, including many well-educated commoners who also joined in.
If they only knew the shadow length, calculating the result would have required proficiency in trigonotry, which could stump most wizards.
But once the vertex angle was known, the calculation turned into basic multiplication and division, allowing even so commoners to work it out!
"The planet’s circumference is forty-three thousand two hundred kiloters, the diater is roughly seventeen thousand seven hundred fifty-one kiloters, and the surface area is five hundred ninety-four million square kiloters?" A mont later, Alec, on the crowded streets of Greenrill City, muttered to himself as he looked at the data he had just worked out.
He was not a wizard, or to be precise, limited by his talents, he didn’t even have the chance to beco a Wizard Apprentice in any magic faction; however, he was deeply interested in mathematics.
In the past, Alec thought math was only sowhat useful in everyday trading—at best, he might beco a tax officer. But the previous issue of "The Magic Daily" opened the door to a new world for him!
That wizard nad Lynn from beyond the Mist Sea planned to asure the circumference of the planet they stood upon without using any magic, relying only on a few simple mathematical formulas!
Alec had originally disbelieved such ease, but when the numbers truly ca to life on paper, any doubt in his heart evaporated, replaced by overwhelming awe. It felt as though the world unfolded under his pen!
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