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This is the geometric relation between π and sqrt(2) In this picture, we can clearly see that the circle's radius is “1”. The side of the pink square is sqrt(2) because 1^2+1^2=c^2, c=sqrt(2). The purple arc on top of sqrt(2) is “π/2”. This picture is a way to calculate π. To Be Continued

Detailed information on the eyesight of butterflies: Butterflies carry proteins called cryptochrome that is sensitive to blue lights Butterflies can see magnetic fields, which is named magnetoception To butterflies, the sky is stripped because they see parabolic, which are the magnetic fields Most of the butterflies can see 4 colors. Some of them can see five or 5 and can see colors we can’t see Butterflies can see UV light, which can help them detect nectar Butterflies can perceive polarized light or light waves that move in only one direction “What Life Is like for a Butterfly.” Anupam Katkar, Anupam Katkar, 28 Jan. 2016, anupamkatkar.com/2016/01/28/butterfly-intelligence-vision-senses/. Accessed 27 Nov. 2022. Undetailed information on the senses of butterflies: touch larvae Touch through hairs that extend through sockets on the exoskeleton Tactile setae are scattered evenly over the whole body Have a variety of responses to touch, which may change over time adult Touch through hairs that extend through sockets on the exoskeleton Tactile setae are scattered evenly over the whole body Specialized setae and nerves can help them sense wind, gravity, and the position of the head, body, wings, legs, antennae, etc hearing larvae Perceive sound through tactile setae Mainly respond to sudden noises (habituation) adult Sense sound through veins in their wings sight larvae Limited and poor See the same range of light as adults See with 12 ocelli adult See with thousands of ommatidia See with compound eyes

The important video that you should watch before reading this article: https://www.youtube.com/watch?v=gB9n2gHsHN4&ab_channel=3Blue1Brown In this article, I will write about how I calculated the dimension of the coastline of Taiwan. I put an image of the Taiwan map with a scale factor of 1 into GeoGebra, and after that, I put 1*1 squares on the places the coastline had touched. As a result, there were 27 squares that the coastline had touched. In the end, it looked like Fig 1, and the number of squares that had touched the coastline in different scale factors is in Table 1. Fig 1 Table 1 According to the video I posted, the graph will be the log of the scaling factor on the x-axis and the log of the number of squares that had touched the coastline on the y-axis, like in Fig 3. So the result should be like in Table 2. Fig 2 Table 2 After drawing the prediction line of Fig Table out, I noticed something was wrong. According to the video I provided, the slope of the prediction line is the dimension of the picture, but the slope of the prediction line is about 0.89, while I think it will be over 1. Maybe I had counted wrong when the number was too big, or there wasn't enough data. Another possible reason is that the squares are not very precise. I should make them smaller. Fig 3

I had done a very simple search about different printers, and this is the mind map I drew. I think that the inkjet printer is the best because it is not very expensive, and its technology is very modern. I think the thermal printer is the least good because I need to buy thermal papers before I can print with a thermal printer which is very inconvenient.

Zero to the power of zero is a very complicated number because people are arguing about whether it is 0 or 1. I am going to give evidence of the three answers.

I found a new way of calculating square roots, and there are some steps to calculate it. I will take the square root of 8465.2347. If you want to calculate a more asymptotic one, you can just keep adding zeros for the number that is being "square-rooted.

How to show the inverse of a function in math? In the mathematical expression, the inverse of "f(x)" will be written as What is the inverse function? Let's look at an example. First, replace "f(x)" with "y", which will turn the function (equation) to Then, switch "x" and "y", the function will be Finally, solve the equation. Let's try another example. Identify if the inverse of a function is a function. First, try to draw the function. Next, draw a horizontal line on the function to see how many intersecting points the function and the horizontal line have. Finally, check if the inverse of the function is a function. If the function and the horizontal line have over one intersecting point, the inverse of the function will not be a function, but if there is only one intersecting point, the inverse of the function is a function. Let's try another example.

When I was doing math yesterday, I saw the "function composition." I decide to understand it and write how to write it and calculate it. I have also written a python program that can draw functions.

The article I read (only summary): https://www.sciencedirect.com/science/article/pii/S2589004222005818 The article is about how light pollution breaks monarch butterflies' circadian clocks. Monarch butterflies think that street lights and other non-natural lights are sunlight. Scientists had done the research and found out this. When the scientists close the lights in the lab, the monarch butterflies will go to sleep, but when the scientists turn the lights on, the monarch butterflies will immediately fly. The picture I had made about the article:

I had a male spider pet named "Spider Asymptotic Bionics." it was initially to mate with a female spider that I had put in its cage. Still, Spider Asymptotic Bionics eats the female spider. I think Spider Asymptotic Bionics ate the other spider because of its hungriness of being locked in a cage with no food all day. Otherwise, I think it is very unusual to see a male spider eating a female spider; they are both jumping spiders. A spider eats food by sucking its prey's juice and meat. After that, it will leave only the prey's shell or exoskeleton. Pictures: Figure1. Spider Asymptotic Bionics is watching you! Figure 2. Spider Asymptotic Bionics was eating the female spider! Figure 3. The exoskeleton of the female spider.

When reading this article, you must look at both the picture and the words.

A website that can help you understand the things that I write in this article:https://en.wikipedia.org/wiki/Shell_theorem

I learned to calculate square root without calculation yesterday. I will explain the method in the next few sentences. For example, I will take the "square root of 2." First, let's define "x=and find the value "a" and "b." "a^2" should be the nearest perfect square number to x, so "a=" because "1^2", which is "1," is the nearest perfect square to "x," which is "2". "b" should be "x-a^2," so "b=1" because "2-1=1". After finding the values of "a", "b," and "x," we can go to the next step, doing continued fraction calculating. The calculation is this, and the more calculation you do, the more the answer will be asymptotic, the true "square root of 2." The formula of the method: algebras: "a", "b", "x" First: "a^2" is the nearest perfect square to "x" "b" is "x-a^2" "x=a^2+b" Second: This is the end of the article. I hope you understand what I have said.

I made a website on my computer that can calculate the up and down of the stock market of Apple Inc, and here are the steps on how to do it. The first step is to observe the data. That means finding data on the stock market. I found the data of the stock market of Apple Inc. on "yahoo finance." The second step is data collection. When I found the data, I had to download it to my computer, so I could use it. Thankfully, people can download most of the data on "yahoo finance." The third step is data processing. If I want to use the data, I found to make a useful thing, I will have to process the data found. This means that I will have to add things to the data, like adding a new list to record whether the stock market of Apple Inc goes up, goes down, or is unchanged. The last step is data calculation. After I had made a new list that recorded the up and down of the stock market of Apple Inc, I had to make a new list to calculate the percentages of the three ways of how the stock market of Apple Inc goes. Here is the website: https://reurl.cc/e30r67

I will point dots on the dartboard. What is the probability of each dot getting pointed? The answer to this math problem is " (1/∞)%", which is officially defined as "0%" because" (1/∞)" is officially defined as "0", but there are two problems in this math problem. First, if the probability is "0%", then none of the points on the dartboard will get picked, but I had still picked 10 points on the dartboard. The second problem is that if all the points have "0%" of getting picked, then the total probability will be "0%", but the total probability should be "100%". A video that can help you understand more about the dartboard paradox: https://www.youtube.com/watch?v=ZA4JkHKZM50&ab_channel=3Blue1Brown

The Monty Halls problem is a kind of game theory. Its game's rule is like this: First, the game judge shows you three doors. There is a car in one door, and there are goats in the other two doors. Second, you choose a door, and then the judge will open one door that has a goat in there, and ask you whether you want to change your choice. Third, the judge will show you whether there is a car in the door that you choose or not, if there is a car in the door that you choose, you in, if there is a goat in the door that you choose, you lose. Will you change your choice, or not? Answer: You should change your choice because you will have more chance of winning. Why: If you do not change your choice, you will have a 1/3 chance of winning. V->door that you choose X->door that you do not choose If you change your choice, you will have a 2/3 chance of winning. V->door that you choose VX->door that you originally choose X->door that you do not choose Further extensions: What are the amounts of goats and cars are different? My programming: output:

Puzzle Simulation is a method to research if there isn't enough equipment, or the research will be nearly impossible to finish if we use the real things to do the research. For example, when researching how monarch butterflies fly, we can't just catch a real butterfly in testing, so we need to simulate how monarch butterflies fly with scientific equipment. We can also use programming to simulate things. Problem For example, I want to know how many chances I will get a "head" if I flip a coin 1000 times, but I can't flip 100 times. It will waste too much time and effort. How can I do it more easily? Project I will program a code and command the computer to calculate how many chances I will get a "head" if I flip a coin 1000 times. (click on the picture below) RAP Simulation Scenarios Interactive Mimics Universe Linear Algebra Analysis Testing Industry Ocean Ecology Simulate Nano Satellites Lufton When I search "simulation" in Lufton, it found three news of the "Monty Halls" problem. The Monty Halls problem is a kind of game theory, too. Reference: https://betterexplained.com/articles/understanding-the-monty-hall-problem/ https://www.statisticshowto.com/probability-and-statistics/monty-hall-problem/ https://en.wikipedia.org/wiki/Monty_Hall_problem

How do social medias give bad effects to people? They will give you low self-esteem. People can post anything they want on social medias if it doesn't break the law. So, you might look at the posts on social medias, envying how life is so great for the people posting the pictures and articles and how poor your life is, but maybe the people just post some fake pictures that trick you into envying them, you life isn't as unlucky and poor as you think it is. They will makes You Mental. As I had said before, social medias bring you low self-esteem and negative feelings and negative feelings do not just effect your studying, work, etc., but make you mental. According to research, children and teenagers who use social media on a daily basis are more likely to develop symptoms of anxiety, depression, narcissistic traits and other mental problems. Young adults who use Facebook are more likely to be anti-social. Conclusion: It is better not to use those social medias, but if you really have to use them, you'll need to have discipline of how much time you'll use them. If you feel that you feel more depressed or have mental problem, you should stop using those social medias for a while and see if you get better, if you don't, then go to a doctor and ask for help. You should not make friends online if you do not see them in real person, there are lots of peoples who are faking to be good-looking and charming on social media and trick you into envying them, or worse, make you do something wrong without noticing, like Tom Riddle's Dairy in Harry Potter until it is too late. "Never too late until it is too late." So stop using those social medias if you can and while you still can.

My teacher invented the game GM5, which I think is very entertaining and educational. I printed and cut these below, which took a lot of time. I also programmed a python code that can print the recommended chip (a small plastic disc used to represent a particular amount of money) placement. related code: full introduction of the game: http://www.davidpublisher.com/index.php/Home/Article/index?id=44288.html

Axiom Theorem Function(Analysis) Equation(Algebra) Formula

When we want to be successful, we need "discipline." Discipline is like personal law. If you have discipline, you will have self-control. For example, if I make a daily plan and follow it every day, I will have discipline. My daily plan in L.A.B. Lab: ▣ Use Lufton for 20 minutes ▣ RAP the word I had searched in Lufton ▣ Read and understand a domino ▣ Read 2 chapters of Rainbow Arch and post the summary on my web ▣ Read 1 paragraph of "Signal Processing for Communications", edited by Paolo Prandoni and Martin Vetterli. ▣ Thinking and Inventing

Today, I change the code of "Traveling Salesman Problem: Solver-Based" from "Matlab help center". The thing I edited was changing the US border to the Taiwan border. I decide to go traveling around Taiwan for half of a leap year with my teacher, Professor Jeng. We'll go to one stop on the map each day. I am very excited about this trip. What the Computer drew: Reference: https://www.mathworks.com/help/optim/ug/travelling-salesman-problem.html

When researching the migration of butterflies, the teacher Jenher Jeng accidentally found a website by a web smart search robot he(Jenher Jeng) invented, named Lufton. The website introduced the gliding of butterflies, how to build a simple wind tunnel, that is a flight simulation, and did a project on a wind tunnel. S.01 Defining a Problem How can change the angle of a butterfly wing relative to the wind, and which angle saves the butterfly the most energy? S.02.5 Hypothesis They use about 45 degrees when they glide because it uses less energy. S.03 Realizing the Situation When I finished reading the website, I found the materials were not very hard to find, and I needed to see which angle had the smallest amount of the lift. How do the butterflies glide: There are four forces the butterfly has when it is gliding: The weight is the force that puts the butterfly down to the ground, for example, the gravity of the earth and the butterfly’s body weight. The lift is the force that pushes up the butterfly and allows it to go upward to stay in the air and have to overcome the weight. The drag is the force that pulls back the butterfly and slows it down while flying. The thrust is the force that allows the butterfly to go forward and go faster, and a butterfly generates it. What is a wind tunnel: People used wind tunnels to do scientific experiments. There are many kinds of wind tunnels, but we will use the wind tunnel shown in “Figure 2.” The angel of the attack is the angle between the butterfly’s wings and the direction of the wind. One thing the scientists tested was how the angle of attack affects the lift of the butterfly. S.04 Stratifying the Factors The things I need to include to build a simple wind tunnel and the paper butterflies that I use to replace the real butterfly: A fan for blowing the wind. Wooden craft sticks to make the butterflies stay still. A hot melt adhesive for attaching the wooden craft sticks. Scissors for cutting some of the wooden craft sticks in half. A protractor for getting the angles right. Two small binder clips for attaching the paper butterfly and the wooden craft sticks. A kitchen scale for measuring the lift. Several heavy objects for making the wooden craft sticks stay still, such as light batteries and heavy tapes. S.05 Collecting the Data I test the angles from 0 degrees to 90 degrees. I write down the reading from the scale every 5 seconds and get the average. S.07 Analyzing the Data I found out that when the butterfly uses 30 degrees to 40 degrees to glide, it will save the most energy. When the butterfly uses 80 degrees to 90 degrees, it will save the least energy. S.08 Refining the Problem If I use different wind speeds, will 30 degrees to 40 degrees still save the most energy? I only use one pair of wings to measure. What if I use two separate teams of attachment? Will the measurement still be the same? I had to use a fan for this science experiment. What if I use the air conditioner or use more fans the next time? What if I change the surface area of the butterfly and its wings? Will the measurement be different? I will use more advanced tools for the wind tunnel. For example, I’ll use an actual 3D printed wind tunnel and natural-sized butterflies next time I do this experiment. I will use more advanced tools like “Arduino Uno” and “Micro: bit” the next time I do this experiment. Reference: https://www.sciencebuddies.org/science-fair-projects/project-ideas/Aero_p049/aerodynamics-hydrodynamics/butterfly-wings-using-nature-to-learn-about-flight?id=860

“An excellent article that shows us the monarch butterflies’ migration.” is enough to describe the fantastic article. Monarch butterflies can not survive the winter like other butterflies. They need migration because their original habitat is too cold for them, and they need to survive by migrating to warmer Mexico. At night, the monarch butterflies roost. While they roost, they huddle together on the tree. Scientists think it helps them get warm, but with other functions. Monarch butterflies need milkweed to survive because they lay eggs on the plant, and their caterpillars feed on them, which is why they are poisonous. In the spring, the butterflies will become active and migrate back up north and east to lay eggs on the leaves of a milkweed plant.

The difference is this:

compose Lufton RAP of CLIMATE & make Links-to-Dominoes

Have you ever considered the implications of this question? "Why are we at war?" is the question. There are several responses to this question. Those of you who are interested in why people fight will find this essay helpful. Primarily, individuals become involved in conflicts because they are ambitious. A government wants to reign over the total area, but they opposed other nations to this. Second, people are at odds because they believe in democracy. They do not want to live under the control of a tyrant. The third reason for conflicts was the outcome of territorial disagreements. In the fourth instance, clashes started because one nation desired retribution against another. In the fifth instance, battles arose because a region wanted independence from the central authority. Finally, religious disagreements are a contributing factor to war. Nazi Germany desired dominance of Europe because it was a visionary organization. Aside from Italy and Vichy France, all the European nations do not want Germany to have sovereignty over the continent of Europe. That was the beginning of World War II. Syrians rejected Assad's tyranny in favor of a democratic government, which triggered the Syrian Civil War. Israel's occupation of the West Bank and Gaza caused the Israeli–Palestinian Conflict to erupt. The United States wished to respond to Al-Qaeda after the September 11th attacks on the World Trade Center. The American Revolutionary War erupted because of the desire of the United States for independence from Great Britain. A religious conflict between India and Pakistan started the Kashmir Conflict. Islam is reviled in India, but it is adored in Pakistan. As said in the preceding paragraph, we understand the reasons for wars, but how can we avoid them? For example, European nations wish to prevent Russia from invading Ukraine, yet Russia continues to occupy it despite international efforts. People will not have enough vision if individuals do not have ambition. Dictatorships will appear in nations if people continue to listen to their leaders and do not fight for their freedom when it is necessary. No one will stop them. Even though battles are destructive, they are occasionally essential for humanity. #