@beachbears564
I adore your presentation. You don't talk down to your audience, you go simply step by step in a clear fashion.
@gbulmer
Susanne, you made that look much more complicated than your usual solutions. You started well by observing all 'red stars' are the same size and the red areas are five times one 'red star', but then instead considered the entire 8 ✕ 8 square! However, one red star is within a 4 ✕ 4 square (16 m^2) with -4 ✕ ¼ circles removed. That's all we need. one 'red star' = 4 ✕ 4 - one (r=2) circle, hence = (4 ✕ 4) - (π ✕ 2^2) = 16 - 12.56 = 3.44, then 3.44 ✕ 5 'stars' = 17.20 (mental arithmetic) Best Wishes. ☮
@JustLilGecko
I subtracted the area of a quarter circle from the 2x2 square, and multiplied by 4 to get a whole star, then by five for all stars
@jcartwrightsmith
This is delightful because Susanne is delightful! Yes, it is fun & rewarding to try to solve these puzzles, but what hooks me is the warmth and friendliness of the presenter. I would never have believed that math puzzles could be so engaging. Kudos to this extraordinary woman!
@darrenhepperle4854
If you circumscribe a 4×4 square around a circle with a diameter of 4 then cut out the circle, the leftover parts can be rearranged and pieced together to make a shape identical to one of our red stars. So I started with the area of a 4m square (16m) and subtracted the area of a 4m circle (≈12.566). This left me with ≈3.434. Five of those add up to 17.168
@CrashOwns
I calculated it like this: Divide the square into 4 smaller squares of 4x4, subtract the area of a cirkel with a radius of 2, multiple the answer by 5: 5×(16-(2^2×π)). Much easier in my head :)
@presidentskroob522
Love this channel! Its an escape from the craziness of the world right now, plus love the accent 😍
@xabiers.3948
I like your channel. The wit and logic are very helpful. Thanks for sharing.
@cognitivefailure
IMO it's a lot easier to visualize an answer if you redraw the figure without the irrelevant bits. Like others, I calculated the area of the innermost "star" by taking the area of the 4x4 square containing the star and subtracting the area of a circle inscribed inside it, and then just multiplied that by 5 to get the final answer. But I think it's easier to see that that's a correct way to approach the problem if you redraw the 4x4 square with only that inner star and leaving out the extra red bits in the corners. Then you can rearrange the 4 remaining quarter-circles like puzzle pieces to get a much more straightforward diagram of a circle inscribed in a square.
@nzaitseva98
It's a beautiful solution to this wonderful problem! I adore your channel and wish you health, happiness and success!
@percarlson927
A+ in visualizing and explaining it so well.
@Skank_and_Gutterboy
This is a nice problem! To do this, I started by deriving the area of 1/4 of a red star, which is the area of a 2x2 square minus 1/4 of a circle with radius 2. So, the quarter-star area is: (2*2) - (1/4)π(2^2) = 4-π. So then, the area of a red star is 4(4-π). The area of all 5 red stars is 5(4)(4-π) = 20(4-π) = 80-20π ≈ 17.168.
@qzorn4440
Another coffee time mystery. I was doing the homework in my head while watching the video and it was very close to your explanation. 🗝️📚 These problems are helping my math thinking a lot. 👍Thank you.
@djparn007
Thank you, Susanne! ❤❤❤❤
@JacquesAltenord
I calculated a rectangle area of 2*4 which contains 1 half circle and 1 half of the 5 areas to calculate. So, the half of one of the five areas to calculate equals 8-2pi. Since the 5 areas have 10 halves, we multiply this by 10. I did this mentally but I love how you break it down.
@Joe-i5z
This left me smiling 😅 That happy math
@jimwetzel1635
Very nice video, as always. Inscribe each red star in a square. At each corner of the square is a quarter-circle, radius 2 m. The square has 4 m sides. The star area is the square area, minus 4 quarter-circle areas. 4 quarter-circle areas is just one circle area. So a red star has an area of (4 m)(4 m) - pi(2 m)^2. Dropping units, that's 16 - 4 X pi. Five stars is therefore 80 - 20 X pi. Unsurprisingly, that's what you got. This is because you're smart, and I'm one of your lovelies. And glad to be, too.
@crosstraffic187
Another good one Math Queen! Thank You
@KinasDevops
Hello Susanne I love your videos and the way you present the solutions, with a perfect explanation at the right time (not too fast, not too long). This 5-star problem is quite interesting and what seemed complex to solve becomes quite simple with the right approach. Here is a nice example how sometimes we think our life is complicated, but then we find that there may be simple solutions :) Continues the excellent work of disseminating mathematics. Greetings from Portugal
@seventhmonkey458