Hi everyone, hope you're doing well! In my previous video, I made a small mistake. Instead of (2 - √3), I accidentally wrote (2 + √3). Fortunately, this didn’t affect the final result since all the calculations were done with the correct value. However, as a perfectionist, I wanted to fix it, and here is the correct version! This just goes to show that none of us is perfect, and we all make mistakes in math. Thank you all for your patience, and I hope you will enjoy this updated video! A big thank you to @RAG981 for spotting that mistake! Great job! Cheers, Phantom of The Math
I always thought that Pac Man's head "split into two" half circles when he opened his mouth. Like when a human opens their mouth, nothing vanishes, just the jaw moves. I would think that Pac Man's head would be 2 semi circles hinged at the left side, which would make the answer the area of the full circle.
Then consider a circle twice the radius of Pacman. With the center at the "neck" apex of the openned triangle. The area of the gob would simply be 30/360 of the double circle's area. Right?
I'll take a stab at deriving a general formula for the Pac-Man puzzle given x and theta. This is maybe a coin flip's chance of being correct but I plugged in sqrt6 for x and pi/6 for theta and it worked, so maybe it's correct. Area of Pac-Man=(x^2*(pi-theta in radians-sin theta))/(2*(1+cos theta)). In square pixels of course! Thanks Phantom for the fun puzzle.
In my previous video, I made a small mistake. Instead of (2 - √3), I accidentally wrote (2 + √3). Fortunately, this didn’t affect the final result since all the calculations were done with the correct value. However, as a perfectionist, I wanted to fix it, and here is the correct version!
@@ThePhantomoftheMath Not even a little phantom is infallable! I've been looking hard for a simplification, like using the midpoint of chord AB to O. But nothing helps improve your solution.
Hey , is there any Formula for the overlapping area of two squares after rotation and translation Like I have a square with a side length of 12 cm. I rotate it by 30 degrees and translate it by 6 cm. What is the area of overlap between its original and final positions?
Hi there! Unfortunately, I think there isn’t a straightforward formula due to the involvement of both rotation and translation. However, you can approach the solution in steps, using geometry and trigonometry. For your example, you can place the square's original position with one corner at the origin (0,0) and sides aligned with the axes. This square extends from (0,0) to (12,12). The rotated square will have its vertices calculated by rotating each original vertex by 30 degrees around the center and then shifting each by 6 cm in the specified direction. Once both square positions are set up in coordinates, you can find the overlapping area by determining the intersection points of the edges of the two squares. This involves solving line equations for the rotated and translated edges with the original square edges. Use polygon clipping (e.g., Sutherland-Hodgman algorithm) to find the overlapping area from the intersected vertices.
@ yeah but it taking so many time this is why i actually asked for a formula , i tried to make a formula , but its really hard to do it , and i don t have any app for that. İn an exam , i want to directly answer that questions with that formula
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Hi everyone, hope you're doing well! In my previous video, I made a small mistake. Instead of (2 - √3), I accidentally wrote (2 + √3). Fortunately, this didn’t affect the final result since all the calculations were done with the correct value. However, as a perfectionist, I wanted to fix it, and here is the correct version! This just goes to show that none of us is perfect, and we all make mistakes in math. Thank you all for your patience, and I hope you will enjoy this updated video!
A big thank you to @RAG981 for spotting that mistake! Great job!
Cheers,
Phantom of The Math
I always thought that Pac Man's head "split into two" half circles when he opened his mouth. Like when a human opens their mouth, nothing vanishes, just the jaw moves. I would think that Pac Man's head would be 2 semi circles hinged at the left side, which would make the answer the area of the full circle.
Then consider a circle twice the radius of Pacman. With the center at the "neck" apex of the openned triangle. The area of the gob would simply be 30/360 of the double circle's area. Right?
Radius of circle :
R= ½c/cos(α/2) = ½.√6/cos15°
R = 1,26795 px
Shaded area : (two circular segments)
β = 180 - α = 150°
A = 2.[½R²(β-sinβ)] = R²(150°-sin150°)
A = 3,4051 px² (Solved √)
I'll take a stab at deriving a general formula for the Pac-Man puzzle given x and theta. This is maybe a coin flip's chance of being correct but I plugged in sqrt6 for x and pi/6 for theta and it worked, so maybe it's correct. Area of Pac-Man=(x^2*(pi-theta in radians-sin theta))/(2*(1+cos theta)). In square pixels of course! Thanks Phantom for the fun puzzle.
I like the PacMan theme, hunting the phantom in the labyrith. You could build on that!
That's a nice idea! 😊
What do you mean sq(6)px? From Greece NGE. Thank you.
Hi! Thanks for watching!
Well, since Pac-Man is in pixels, I just wanted to make a joke with units. Nothing more. 😊
My dumbass tought it was pi×{[SQRT(6)]/2}² .
(6)^2=36 36/30 1.6 1.2^3 1.2^1 2^1 (x ➖ 2x+1).
Why was this video deleted, and then re-uploaded a couple of hours later?
Check my comment please! :D
In my previous video, I made a small mistake. Instead of (2 - √3), I accidentally wrote (2 + √3). Fortunately, this didn’t affect the final result since all the calculations were done with the correct value. However, as a perfectionist, I wanted to fix it, and here is the correct version!
@@ThePhantomoftheMath Not even a little phantom is infallable!
I've been looking hard for a simplification, like using the midpoint of chord AB to O. But nothing helps improve your solution.
Hey , is there any
Formula for the overlapping area of two squares after rotation and translation
Like
I have a square with a side length of 12 cm. I rotate it by 30 degrees and translate it by 6 cm. What is the area of overlap between its original and final positions?
Hi there! Unfortunately, I think there isn’t a straightforward formula due to the involvement of both rotation and translation. However, you can approach the solution in steps, using geometry and trigonometry.
For your example, you can place the square's original position with one corner at the origin
(0,0) and sides aligned with the axes. This square extends from (0,0) to (12,12). The rotated square will have its vertices calculated by rotating each original vertex by 30 degrees around the center and then shifting each by 6 cm in the specified direction.
Once both square positions are set up in coordinates, you can find the overlapping area by determining the intersection points of the edges of the two squares. This involves solving line equations for the rotated and translated edges with the original square edges. Use polygon clipping (e.g., Sutherland-Hodgman algorithm) to find the overlapping area from the intersected vertices.
@ yeah but it taking so many time this is why i actually asked for a formula , i tried to make a formula , but its really hard to do it , and i don t have any app for that. İn an exam , i want to directly answer that questions with that formula
@ so by any chance could u find it ?
@@luyrian1280 You want me to solve this problem?
@@ThePhantomoftheMath yeah
I didn't notice the acknowledgement to me of helping you by pointing out your error. I may not be so sympathetic in future. ☹
Excuse me, but it seems like you didn't read my post or my comment carefully. I mentioned you in both and thanked you for pointing out the mistake.
I always try to stay true and acknowledge someone's success ,and good will. And thanks again!
Me feel feelings too! Screen not do I want. Stupid screen!
Then we get a bit real again, right?