I made science magic

After hearing what Lin En said, Lydia's originally happy expression immediately froze, and then she looked sad. She had to join Yieta College to learn this knowledge, but the key was that she had to fly to the sky first to pass the test...

This seems like an endless cycle...

"If you can build the airship perfectly according to the design, then for the first flight, we can consider letting you fly it." Lin En said with a smile. "I remember that the agreement between you and Master Hellram was to fly in the sky without using magic, which barely meets the requirements."

"Can I really fly it?" Lydia jumped up excitedly, and then bumped her head against the wing frame. The pain made tears well up in her eyes, but she still covered her head and looked at Lynn eagerly.

"Of course, but let me be clear first, my requirements are very high!" Lin En said calmly.

Although one of his purposes this time was to trick... ahem... recruit this half-ling girl as his assistant to help him make and sell those novel creations, thus saving more time to study magic.

But the way and method of doing things is also very important. If you just go to someone's door and invite them to help you, it may arouse suspicion and will not achieve good results.

Only opportunities that are gained through one's own efforts will be cherished by others, and they will be more serious in studying Olympiad mathematics in the future.

Chapter 68: Excited Wizard Apprentices

Just as Lin En thought, the extremely high requirements did not scare Lydia away. Instead, it made the half-orc girl more motivated and she looked at the design drawings very seriously.

After learning that making an airship requires some light and tough materials, Lydia immediately suggested using camel leather that has been soaked in water and dried to make the airbag of the airship. This material meets the requirements very well and is usually used in the sails of large warships.

On the foggy sea, the sails of the warship they sailed were made of camel leather. No matter how big the storm was, it could not destroy it. It was very durable and reliable.

The frame of the airship airbag can be made of the branches of the magic tung tree, which has high tensile, compressive and bending strength...

Lydia talked incessantly. In the field of aircraft design, she was far inferior to Lin En, but she knew the characteristics of various materials in the other world very well.

Lin En silently calculated in his mind that if the airship was made according to the materials Lydia mentioned, the performance of the airship would definitely be improved a lot, but the cost would also become extremely high.

At least one hundred magic gold coins are needed...

Lin En thought about his savings and coughed twice, interrupting the girl's words. "Actually, this airship is just an experimental version. It doesn't use such good materials. A nearly good one will do!"

"How is that possible? This is the first airship that can fly and turn in the sky." Lydia said with longing.

“I can only give you twelve magic gold coins as a deposit.” Lin En said helplessly, and took out a purse. This was one of the few assets he had. The rest of the money would have to be filled when there were more students in the Olympiad Mathematics class, and then he could apply for some teaching funds from Hellram...

Lydia shook her head and refused to accept it. The new knowledge that Lin En explained to her was worth more than a hundred magic gold coins. Moreover, this airship was directly related to whether she could enter the Yieta Magic Academy.

"The money for making the airship can be considered as tuition for the lecture. I will use the best materials to build it. Let's start now!" Lydia wiped the stains off her face and asked Darren to call the rest of the halflings in the workshop. She wanted to complete the construction of the airship within a month.

Looking at the halflings who were busy working, Lin En wanted to help, but was stopped.

The use of magic might leave traces, and it would be bad if Master Hellram thought that the airship was suspected of being built with magic. Besides, Lin En was a customer, and there was no reason to let a customer do it himself.

In view of this, Lin En, who had nothing to do, could only take charge of the command and watch those halflings, who were only half his height, running around carrying wood that was heavier than themselves.

……

The progress of airship production was faster than Lin En had imagined. After working all night, one-sixth of the overall frame had been built. If it weren't for the large amount of camel leather used to make the airbags that required special processing, which took a lot of time, it would probably take less than a month to build the airship.

However, such rapid progress was not without cost. The halflings were almost exhausted, as all their previous enthusiasm had been put into their work.

Darren was lying on a solid wooden board and snoring. Lydia was even more exaggerated. She slept directly on the frame of the airship, holding a beam tightly, with saliva at the corners of her mouth, and she muttered something from time to time.

Lin En shook his head and immediately stopped several halflings who were still busy. He moved Lydia and others who had fallen asleep into the house and let them have a good rest.

After becoming a wizard apprentice, not sleeping for a night did not have any effect on Lin En's spirit, so after settling Lydia, who fell asleep due to exhaustion, he left the workshop directly.

After a whole day, Lin En was looking forward to seeing whether the wizard apprentices could solve the exponential formula he left behind.

Pushing the door and walking into the classroom, Lin En saw all the confiscated coins piled up on the desk. What surprised Lin En was that the classroom, which seemed a little empty in the last class, was now packed.

A quick glance showed that there were at least 150 to 160 people. If the classroom wasn't big enough, I'm afraid they wouldn't be able to accommodate all of them.

Is an index game so useful?

"Good morning, everyone!" Lynn's mind was full of thoughts, but he didn't show any of them on the surface.

However, the students' reactions were more enthusiastic than he had imagined.

"Professor Lin En, are there any other Olympiad math problems?"

"I have already calculated the numbers for the thirty-six and forty-nine squares..."

……

Looking at the extremely excited wizard apprentices in the classroom, Lin En was completely shocked. Could it be that all the students at Yieta Magic Academy were a bunch of masochists?

I'm so passionate about math...

No, something must have happened that I didn't know about.

Lin En thought about this, but he was not in a hurry to confirm it. Instead, he turned to look at Alok and asked. "It's been a day now. I believe you should have the answer, right? Alok?"

"Professor, the sum of these thirty-six squares is six hundred and eighty-seven billion nineteen million four hundred and seventy-six thousand seven hundred and thirty-five..." Alok stood up hurriedly and answered tremblingly.

He had confirmed this number many times, counting twenty pages, but the final amount was too large and he only had one chance to answer. If he got a number wrong, he would be doomed.

Under Alok's anxious gaze, Lynn nodded.

"Very good, that's correct."

"Have you figured out the meaning of the formula I gave you?" Lynn asked again.

"I have figured it out. The sum of the numbers in the squares is equal to twice the last digit minus one!" Alok said confidently. After he no longer had billions of debts, his lost confidence was restored.

In order to get the correct result yesterday, he calculated for a whole night, and it was through repeated confirmation that he discovered this trick.

Lin En nodded again. With little mathematical knowledge, it was considered a barely acceptable achievement to be able to find this pattern in one day.

"Professor Lin, can I get the bonus?" Alok asked expectantly.

Pierce and the others looked at Alok with envy. That was twenty magic gold coins. Although they had calculated for a long time yesterday, they were not as desperate as the other party and could not find the pattern first.

Lin En naturally knew that Hellram had offered a reward for the formula he wrote, but due to his professor's reserve, he was reluctant to take it himself.

But it is still a long way to go to get the money just by relying on the few patterns found!

"Eloquel, my summation formula is not that simple. What if I slightly modify the rules of the grid game, for example, the number in the next square must be three times that of the previous square? Will your theory still apply?" Lynn asked with a smile.

The smug expression on Alok's face froze instantly. He immediately started to do some calculations in his mind, and then picked up the quill to write and draw on the papyrus...

"What if we add another rule that you need to place seventeen copper coins in the first grid?" Lin En asked again.

Alok completely collapsed, his mind was filled with a huge amount of numbers...

This is too difficult!

He couldn't figure it out at all!

Chapter 69 How many math Olympiad problems did you solve to achieve what you have today?

Lin En's two short sentences brought Alok down from heaven to hell, and the students present shuddered.

“Mathematical Olympiad is an extremely sophisticated course. We need to find the patterns in a large amount of extremely complex data calculations, and then summarize them into corresponding formulas to simplify the algorithms and improve the efficiency of the entire calculation.” Lynn looked around at everyone in the classroom, paused, and spoke again.

"Of course the law that Alok summarized is not wrong, but the scope of its application is too small. Since the exponential increase in the square can be 2 times, it can also be 3 times, times, or times! In this way, this law is no longer applicable..."

"And this exponential summation formula is applicable to all exponential increases that meet the conditions!" Lin En snapped his fingers, and under the surge of magic power, the complicated formula appeared in front of everyone again.

When q≠1, Sn=a1(1-q^n)/(1-q)

Johnny, Peirce and others stared at the so-called exponential sum formula, pondered for a while, and then picked up their quills to start calculating, listing series of two, three, and four times, looking for the patterns in them, and then trying to substitute them into the formula.

With Alroch's previous summary, and through deduction through q≠1, Peirce quickly realized that this symbol should refer to the multiple of the amplification, but why use one to subtract?

Peirce bit his finger and substituted the initial double-growing square game into the equation, ignoring the (2-q) at the end and performing the calculation directly. He found that it worked, but the resulting number was exactly the opposite, a negative number.

In other words, does the function of the following formula is to convert negative numbers into positive numbers?

But if it were a 3x exponential growth, the number would be completely wrong...

Peirce's brain was working rapidly, and he had already vaguely grasped the answer. It was almost there, just almost there!

But what is it?

Throughout the classroom, there were many people like Peirce, concentrating on doing the exercises, some pulling their hair, some scratching their ears, but no one chose to slack off and give up.

Is the learning atmosphere at Yieta Magic Academy so rich?

Lin En was somewhat puzzled. These people were too fond of studying...

Most of the class passed quickly, and just when Lin En thought that there would be no results today, a hand was raised high.

"Professor Lynn, I have some ideas!"

It was Johnny who spoke. After receiving the instruction, the girl stood up and said, "In the summation formula, a1 should refer to the number of the first square, q refers to the multiple, and n corresponds to the number of squares, right, professor?"

"That's roughly correct. After class, you can go to the entrance of the academy to collect your reward!" Lynn nodded in response. Although Johnny's statement was very general, it was indeed accurate.

Pierce on the side could not help beating his chest and stamping his feet. After Johnny's reminder, he quickly understood why. It was just a little bit short. He was about to solve it!

After waving his hand for Johnny to sit down, Lynn began to explain to the apprentices present what a geometric sequence is, its general term, and summation formula, and then went on to explain how each formula was deduced.

The wizard apprentices below all picked up their quills very seriously and wrote down every word Lin En said on the paper. Then they tried to change the first term and multiples to verify it repeatedly. The desks were soon filled with various manuscripts...

It has to be said that with the general formula and the summation formula, the speed of calculation is several times faster, and the more complex the formula is, the faster the improvement.

Looking at these students who were more enthusiastic than each other in doing the exercises, Lin En couldn't help but sigh that being a professor was too easy!

If the situation in federal schools is the same, why should we worry about the development of science and technology?

……

The second Mathematical Olympiad class ended quickly. Alok and the others left the classroom reluctantly, still discussing the derivation of the summation formula...

"Johnny, how much magic power have you been able to control increased from last night to now?" A black-haired witch apprentice came up, patted Johnny on the shoulder, and asked curiously.

"About 10%?" The silver-gray-haired girl thought for a moment and replied casually.

"That's a little more than me." The black-haired witch apprentice curled her lips, but there was no envy on her face.

According to rumors, Alok calculated all night without sleep, and when he woke up the next day, he found that the magic power he could control had increased by about 20%. It was this news that set off the entire Yieta Magic Academy.

So this morning, all the wizard apprentices who had no classes came, wanting to hear what kind of magical power this so-called Olympiad math class had, and she was no exception.

The conclusion is also obvious. Complex and tedious mathematical operations can effectively exercise their brain power. The process of logical deduction, finding and cracking numerical patterns is also interesting, at least more interesting than boring meditation.

Johnny ignored the black-haired witch's words and looked back in the direction of the classroom, secretly wondering how many math problems Lin En had solved in the [Secret Law Society] in the past six months to achieve today's achievements...