Game "SineRider" which helps to understand intuitive mathematics by visualizing mathematical expressions

Most people finish studying mathematics without understanding the beauty of mathematical formulas, but there are some people who can feel that only a few "mathematics are beautiful", and how can we see mathematical expressions I think. It is easy to imagine such a mysterious formula, it is a game sense to polish the sensitivity of mathematics "SineRider"is.

About SineRider
http://sineridergame.com/

This time install SineRider on a Windows PC and try using it. Click "Download for Windows" at the bottom of the page.


Save the ZIP file to your favorite place such as desktop,ExplzhThen use SineRider.exe in the folder to start SineRider.


SineRider's startup screen looks something like this. Clicking on the green triangle mark will bring up a graph of a complicated mathematical formula below and a movie will start that two people riding the sled at the center of the screen will slide. SineRider is a game where you compete for the time to enter a mathematical expression, make a graph and go through the designated point through the sled.


When you move the mouse cursor over the screen, click "The Basics" under "Welcome" of the coming bar.


Then, the specified point appeared in (0, -8) of X and Y coordinates. It is OK if you enter a formula in the text box at the bottom of the screen so that you can move two people riding a sled to this coordinate.


For example, if you enter "y = - 20" and click the triangle icon ... ...


A graph of y = -20 appears and the warp passes through the designated point with free fall.


Clearly clear. The time was 1.7 seconds. Click "Next Up: Constants" to advance to the next subject.


Next, three designated points appear on the y coordinate. On the graph "y = -5" ......


Sori can fall only to the graph of y = -5, it will not be cleared as it can not pass through the point below it. Even though it is heartless, time will progress without stopping, but of course clearing can not be done even if waiting as it is.


Enter "y = -20" again.


Then the warp falls to the straight line of y = -20, passed through the designated point one after another and it cleared safely.


In the next issue, the numbers "A", "B" and "C" are both "3". It is necessary to stay at least 3 seconds at the point of "3" while passing through "A → B → C".


Therefore, on the same "y = - 20" graph as before, I passed the point "3" and failed because I can not stay for 3 seconds.


So enter "y = -15" so that the graph will come close to the "3" point.


Clearly clear.


Of course, the graph can be cleared by creating a "bottom" using a parabola (quadratic function) like "y = - x ^ 2 - 15" as well as a straight line (linear function).


The next problem is that the points are lined up with a downward slope. In the graph "y = x - 2" you are now entering, the warp slips in the lower left direction and you can not clear it.


So change "y = -x-2" and the slope of the graph ...


clear.


Set the slope to "-1 / 4" ...


Adjust the position of the y intercept while decreasing the tilt. As I am clearing the game, my memory of junior high school math gradually revives.


I am not satisfied with just a straight line, challenging the tutorial "Parabolas (parabola)".


Adjust vertices and y intercepts of quadratic function graph ... ...


clear.


This is a problem conditioned two points of rolling down ○ and "1" requiring a stay of 1 second or more.


Clear by placing the graph in this form. Since the shape of the graph changes each time you change the formula (numerical value) to be entered, you can intuitively understand "what kind of parameters will change if the parameter changes?" Even if you look at the textbook, even people who were tedious in mathematics are playing with SineRider, it seems that they can somehow understand the meaning of the formula.


Click the tutorial on "Waves (Wave)".


A problem to clear by using such a waveform (trigonometric function) appeared. In this problem it is ok to hit two falling ○ with sled. In other words, it would be nice to drive two ○ marks into trigonometric "valley".


If you mess with the mathematics and place mountains and valleys like this ... ...


Sori and two ○ ○ successfully gathered in the valley successfully cleared.


This graph also ....


You can change the graph by changing the formula a little.


Try clicking "Out of Order" ......


Such a problem from the first question. It is natural that warp can not be advanced in the lateral direction easily, impossible to say that it is necessary to pass points in order of A → B ......


SineRider is easy to understand how the graph changes when you tamper with the parameters of mathematical expressions It can be said that anyone who is good at mathematics or who is not good at mathematics can "enjoy mathematics" games.

Incidentally,Unity PlayerYou can also play SineRider on the browser by installing it.

SineRider
http://sineridergame.com/SineRider.html