Okay, so the Riemann Sum does the same thing that an integral does, as it is essentially measuring the area under a curve! What this means for 𝛑, is that you can measure the area (well, approximate the are) of a semicircle, multiply it by 2 to get the area of a circle, and divide by r**2, to solve for an approximate value of 𝛑!

To imagine the Riemann Sum properly, think of a semicircle, with both ends touching the x axis. Now, imagine this:

This is a good visualization of integration (or more specifically, the Riemann Sum), but what is actually going on?

Well, there are two ways to explain this: The Calculus way, or the Summation way.

First off, the Calculus method is fairly concise and easy to read, but does not really help all that much:

Cool, right? (Note from after I took that photo, the integration is not approximately the area, it is exactly the area.)

Now, the Summation way (aka the Riemann Sum) makes all this so much clearer!

(In case you do not know how to read this one, it is basically saying that, as n → ∞, it sums all of the areas of all n rectangles that fit under the curve.)

Note that, when plugged into a calculator, you can say:

Please let me know if you have any further questions!!! ^ ^*

Oh, also, please pardon my poor penmanship.. T ~ T I have not written English too much lately. (Lol)

@CodingCactus Oh, thank you for asking! Quite well, actually. I'm making steady progress on the sprites, I may be able to (if I work a lot on it) finish the first 30 to 40 sprite sets by next week! ^~^*

@AmazingMech2418 Sorry for the really late response, I haven't been on here as much unfortunately... It is going pretty well, since I started using the IDLE Python program. I can now use multiple files, turtle, AND properly use the sprite converter you made! I've started work on the most important parts though, including:

Type effectiveness system

Proper damage calculation

Bag system (I have just barely started this, though.)

Turn system for battle, and status effects that affect the initiative order

Got any ideas on ways I could do these easily? Thanks ^ ^*

In Pokemon, each different pokemon has one or two types (so Grass, Fire, Water, etc). Some types are super effective against others, and vice versa.

All this means is a way to calculate how much damage a move would do to the enemy, that is accurate.

The bag is just the player's inventory.

I mean a turn-based fighting style like there is in Pokemon. There are some status effects that affect the order in which the pokemon make their moves.

@LizFoster Well, for the type effectiveness part, you could probably just use a list or dictionary with values for the effectiveness and use those values to determine the damage per attack (or whatever is needed in Pokemon. I'm not really sure).

For the "bag" or inventory, you should be able to do a dictionary with all of the different items and their quantities and, when an object is picked up, increase the quantity by 1, and when an object is used/discarded, decrease it by 1. If there is a finite size, you could do that you can't pick up an object if the sum of all of the quantities is greater than a certain value, or the sum of the products of the quantities and a separate variable to determine the amount of space it would take up.

Then, for the turn-based fighting system, I'm still not completely sure what you need help with (the AI, the player, the overall UI?).

@AmazingMech2418 Hm, good idea. THe only problem now is, how am I supposed to find what every trainer's pokemon are? I don't have a copy of the games, so this might prove a bit more challenging than the more simple stuff, such as trainer AI, or a list of all of the items (and their functions).. T~T

@AmazingMech2418 Also on a high note, I've finished plugging in all of the front sprites for all of the pokemon! Now I just have to delete the old and unnecessary files, and do the same for all of the back sprites. Hooray! :D

@AmazingMech2418 Well, along the way on your journey in the game, you run into a bunch of NPCs, or trainers as they are called. They all have teams of their own pokemon.

@AmazingMech2418 That could make for a rather interesting game, actually! (Lol) Although, another tactic comes to mind. I could watch a few play-throughs of the game, as well as look through the Pokemon wikis. Those might help for the major trainers, and for the minor ones, I could probably just randomize them based on the surrounding available pokemon...?

## The Riemann Sum!

Let's talk about the Riemann Sum!!

Okay, so the Riemann Sum does the same thing that an integral does, as it is essentially measuring the area under a curve! What this means for 𝛑, is that you can measure the area (well, approximate the are) of a semicircle, multiply it by 2 to get the area of a circle, and divide by r**2, to solve for an approximate value of 𝛑!

To imagine the Riemann Sum properly, think of a semicircle, with both ends touching the x axis. Now, imagine this:

This is a good visualization of integration (or more specifically, the Riemann Sum), but what is actually going on?

Well, there are two ways to explain this: The Calculus way, or the Summation way.

First off, the Calculus method is fairly concise and easy to read, but does not really help all that much:

Cool, right? (Note from after I took that photo, the integration is not approximately the area, it is exactly the area.)

Now, the Summation way (aka the Riemann Sum) makes all this so much clearer!

(In case you do not know how to read this one, it is basically saying that, as n → ∞, it sums all of the areas of all n rectangles that fit under the curve.)

Note that, when plugged into a calculator, you can say:

Please let me know if you have any further questions!!!

^ ^*

Oh, also, please pardon my poor penmanship.. T ~ T I have not written English too much lately. (Lol)

@LizFoster, how is Pokemon violet going btw?

@CodingCactus Oh, thank you for asking! Quite well, actually. I'm making steady progress on the sprites, I may be able to (if I work a lot on it) finish the first 30 to 40 sprite sets by next week! ^~^*

@LizFoster very nice!

@LizFoster Wow! That's a lot faster than it was when you were doing it by hand...

@LizFoster How's your game going now?

@AmazingMech2418 Sorry for the really late response, I haven't been on here as much unfortunately... It is going pretty well, since I started using the IDLE Python program. I can now use multiple files, turtle, AND properly use the sprite converter you made! I've started work on the most important parts though, including:

initiative order

Got any ideas on ways I could do these easily? Thanks ^ ^*

@LizFoster I'm not sure exactly what you mean by each of those. (sorry, but I've never played a Pokemon game before) Could you explain what you mean?

@AmazingMech2418 Okay, so:

Grass, Fire, Water, etc). Some types are super effective

against others, and vice versa.

would do to the enemy, that is accurate.

There are some status effects that affect the order in which

the pokemon make their moves.

So sorry, does this help at all? o~o

@LizFoster Well, for the type effectiveness part, you could probably just use a list or dictionary with values for the effectiveness and use those values to determine the damage per attack (or whatever is needed in Pokemon. I'm not really sure).

For the "bag" or inventory, you should be able to do a dictionary with all of the different items and their quantities and, when an object is picked up, increase the quantity by 1, and when an object is used/discarded, decrease it by 1. If there is a finite size, you could do that you can't pick up an object if the sum of all of the quantities is greater than a certain value, or the sum of the products of the quantities and a separate variable to determine the amount of space it would take up.

Then, for the turn-based fighting system, I'm still not completely sure what you need help with (the AI, the player, the overall UI?).

I hope this helps!

@AmazingMech2418 This certainly does help! Thank you! For the turn-based fighting, I was referring more specifically to the AI.

@LizFoster For the AI, I guess you could just use a system to evaluate all possible moves and use a pseudorandom number generator to choose the move?

@AmazingMech2418 Hm, good idea. THe only problem now is, how am I supposed to find what every trainer's pokemon are? I don't have a copy of the games, so this might prove a bit more challenging than the more simple stuff, such as trainer AI, or a list of all of the items (and their functions).. T~T

@AmazingMech2418 Also on a high note, I've finished plugging in all of the front sprites for all of the pokemon! Now I just have to delete the old and unnecessary files, and do the same for all of the back sprites. Hooray!

:D@LizFoster Nice! Though, what do you mean by "what every trainer's pokemon are"?

@AmazingMech2418 Well, along the way on your journey in the game, you run into a bunch of NPCs, or trainers as they are called. They all have teams of their own pokemon.

@LizFoster Okay. So, you don't know what pokemon are in each team? Maybe, you could randomize it or something? I don't know.

@AmazingMech2418 That could make for a rather interesting game, actually! (Lol) Although, another tactic comes to mind. I could watch a few play-throughs of the game, as well as look through the Pokemon wikis. Those might help for the major trainers, and for the minor ones, I could probably just randomize them based on the surrounding available pokemon...?

@LizFoster I think that would work!

@AmazingMech2418 Sweet! Also, I just found a page that lists how stats are calculated!

@LizFoster Nice!