Geometry – power of a set of points to determine the inradius of a right triangle.

The question is:

Prove that the inradius is a right-angled triangle with leg lengths $ a $ and $ b $ and hypotenuse $ c $ is $ (a + b-c) / 2 $

When I drew a picture, I found that certain lengths were the same as the set, that tangents from the same point are the same, but I am not sure how to proceed. Any ideas?

Get 56 points – EASY TASK

Manual:
1. Open the video and like it.
2. Play the video to the end.
3. Comment out the video.
4. Come back and answer your Youtube username so that I can verify the reward and send it to you.

Code:

https://www.youtube.com/watch?v=WQCOWTUXiNQ

Get 57 points – EASY TASK

Manual:
1. Open the video and like it.
2. Play the video to the end.
3. Comment out the video.
4. Come back and answer your Youtube username so that I can verify the reward and send it to you.

Code:

https://www.youtube.com/watch?v=oYXoiCODXBY

Applications – How often does Waze update points in the map while driving?

Today, before I drove to work, I opened Waze and as expected gas stations were displayed near me.

I then noticed that the map still showed the old points after 16 km. The map has not been updated. I had to close and open the app to see the new points near me.

My Question: How often does Waze update the map while I drive?

Many Thanks.

Get 59 points – EASY TASK

Manual:
1. Open the video and like it.
2. Play the video to the end.
3. Comment out the video.
4. Come back and answer your Youtube username so that I can verify the reward and send it to you.

Code:

https://www.youtube.com/watch?v=EjMpt5laJmE

Get 58 points – EASY TASK

Manual:
1. Open the video and like it.
2. Play the video to the end.
3. Comment out the video.
4. Come back and answer your Youtube username so that I can verify the reward and send it to you.

Code:

https://www.youtube.com/watch?v=DL8cvYxJBys

Discrete Math – Find critical points, uncritical points, and saddle points using a contour plot

Thank you for writing a reply to Mathematics Stack Exchange!

  • Please be sure too answer the question, Provide details and share your research!

But avoid

  • Ask for help, clarification or answering other questions.
  • Make statements based on opinions; Cover them with references or personal experience.

Use MathJax to format equations. Mathjax reference.

For more information, see our tips for writing great answers.

numerics – Calculates the distance between two points and determines the direction

I program a molecular dynamic program with periodic boundary conditions. Here I have a problem:

I have a list of coordinates like

list = RandomReal[{0, 1}, {5, 2}]

And now I want to have the distances.

I'm doing that

EuclideanDistance @@@ subsets[list, {2}]

But now I do not know the direction, so if the distance was not positive or negative to the square.
Does anyone know how to get the sign?
Because I need that for calculating my periodic boundary conditions

Architecture – Synchronize points from the user interface and from the server

I'm sorry in advance if it's not clear.

I would like to make a game with the following map (in reality, it will be a 3D globe).

Enter image description here

Now this map contains a point and each point is a place where the user can build something.

Enter image description here

The distance between the points is very important and also the position of the individual points (not on the water and equidistant from each other).

The problem is that I do not know how to sync the item with the server. to explain:

I want the point to be the same distance apart and only in the countryside. Generating them is quite simply out of the game. but since the game will have a server that controls what each builds up by multiple players, i should generate them on the server. but I do not know how to do that. since only the game itself knows the map and where it can place the point.

Should I generate them in the game, then copy the amount I can fit and write them on the server as if I could fit 200 points. I'll let the server generate 200 points with an ID of 0 to 200 and the UI will draw them in turn.

I need a little help to find the right direction.

Many Thanks