Though this tool was invented by the ancients, one must admit, it indeed possesses a convenience apparent to the naked eye.

Therefore, after careful consideration.

Xu Yun ultimately decided to first introduce the concept of Arabic numerals.

Considering the calculations needed in the future are bound to be quite substantial, having a convenient tool would certainly make things easier; efficiency being higher is naturally better.

Of course.

Although Jia Xian did not recognize Arabic numbers and symbols, this does not mean he did not understand these concepts:

Quite the contrary.

Whether it's addition, subtraction, multiplication, division, or square and cube roots, ancient Huaxia mathematicians had long been studying them.

Thus, it took almost no time for Jia Xian and Old Su beside him to quickly understand and accept Arabic numerals.

And after understanding the content of the letter and the related mathematical concepts, Jia Xian somewhat calmed down, not as irritable as before.

He cleared his throat lightly, then subtly put away the letter and Xu Yun's paper, and said to Xu Yun:

"Alright, Wang Lin, you went to such lengths to lure this old man to Bianjing, surely it is not just to introduce Arabic numerals, is it?"

In ancient Huaxia.

Although the mathematics circle did not have BBS or forums like in later generations, under the organization of some highly respected and well-off bosses, regional communication was quite common.

Even in the Jiangnan Region, a small-scale publication akin to a mathematics newspaper started to emerge.

This kind of publication was very cheap, costing only a few coins to subscribe, and was printed about once a month.

Considering the cost of paper, transportation, and printing at this period, this price was basically akin to selling at a loss.

In short.

If Xu Yun merely wanted to publish his findings, he could easily make his solutions public by using the connections of Old Su to contact a few 'editors'.

Therefore, it was very obvious.

The reason Xu Yun went to such great lengths to 'trick' himself into coming to Bianjing must be because he had a request.

Xu Yun did not keep him in suspense, he paused briefly, then bowed slightly to Jia Xian and said:

"This time, inviting Mr. Tongyu here, I indeed have an important matter, hoping sir could lend a hand."

"What matter?"

"Studying the lens formula."

Jia Xian was taken aback at once and blinked his eyes vacantly:

"Lens? Formula?"

The latter could be understood, but what on earth was the former?

Old Su, who was beside them, upon seeing this, immediately took out a roughly polished lens from his sleeve pouch and handed it to Jia Xian:

"This is the object."

Jia Xian took the lens and examined it for a while, contemplating:

"It seems like Ai Dai, but both sides are fuller, yet judging by the material... it also seems to be made of glass?"

Xu Yun nodded:

"Correct."

Jia Xian's eyes filled with increasing puzzlement:

"But what does it have to do with a formula?"

Xu Yun was silent for a moment, then said:

"Mr. Tongyu, I have heard you say once, 'The myriad things in the world, each has its inherent reasoning', is it not?"

Jia Xian nodded gently, this saying was somewhat a motto of his life:

"Correct."

"So have you ever thought... the light we see every day might also have some undiscovered reasoning?"

Jia Xian's pupils immediately constricted, and he instinctively looked out the window:

"Light?"

Xu Yun thought for a moment, then took paper and pen.

He drew a right-angled triangle with its right angle facing the right and its base at the bottom.

He then drew several lines on each side, sequentially marking them with the words "Sun, Moon, Mountains, Winter Green, North Heart," totaling 22 characters.

He then drew an inscribed circle and narrated while writing:

"Mr. Tongyu, from the center of the circle, vertically and horizontally extracted, one can get fifteen shapes, all without oddity."

"The three vertices are, respectively, Heaven, Earth, and Qian; the incenter of the Heaven-Earth-Qian triangle is called the Heart."

"A vertical line passing through the Heart intersects the triangle and the incircle at Sun, South, and North points respectively."

"A horizontal line passing through the Heart intersects the triangle and the incircle at River, East, and West points respectively."

"The vertical line passing through East and the horizontal line passing through South are both tangents to the incircle, they intersect the Heaven-Earth-Qian triangle at Gen, Kun, Mountain, and Moon four points, intersecting each other at Xun point."

"Qian, Kun, Xun, and Gen four together can form a square."

"The vertical line passing through the Moon intersects the East-West horizontal line at the Green point, and the Ground-Qian edge at the Spring point. The horizontal line passing through Mountain intersects the North-South vertical line at the Vermilion point, and the Sky-Qian edge at the Gold point. These two lines intersect at the Fan point."

"Finally, the horizontal line passing through the Sun intersects the Sky-Qian edge at the Dawn point, and the vertical line passing through River intersects the Ground-Qian edge at the Dusk point."

"The above points total 22."

When Xu Yun initially started drawing, Jia Xian's gaze was somewhat casual.

He didn't understand why Xu Yun, while speaking about light, would divert the topic to a triangle.

But as he watched.

His expression gradually became more serious.

By the end.

Only one emotion remained on his face...

Astonishment!

As an expert in triangular problems, Jia Xian had proposed an idea... or rather a theory, many years ago:

"The sum of the legs and the hypotenuse is harmony, the difference is contrast, equality is change, for multiplication, for segments, squared is the product, is the power."

This is the famous Thirteen Diagrams of the Pythagorean Reply:

Referring to the leg (a), another leg (b), hypotenuse (c), the contrast of legs (b-a), contrast of leg and hypotenuse (c-a), contrast of hypotenuse and another leg (c-b), sum of legs (a+b), sum of leg and hypotenuse (a+c), sum of hypotenuse and another leg (b+c), contrast with hypotenuse added (c+(b-a)), sum and contrast with hypotenuse (c+(a+b)), sum and contrast (a+b)-c), contrast contrasted (c-(b-a)).

One can say this.

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