Well it will apply in shapes with a 90 degree triangle ofc. Squares and rectangles sure, but not trapezoids or kites and such (at least not all of them
I can't remember ever learning that an inscribed triangle along the diameter is a right triangle, but it makes sense. That's the conceptual step I was missing.
@@Zieki99 Not that I can recall, but highschool was more than a decade ago and I don't use geometry in my day-to-day job. Again, it's just something I can't remember ever being covered, not that we didn't cover it.
The last time I needed to solve problems like this was around 15 years ago, but i still come here and try to solve these once in a while. The way you teach and explain is so good! Kudos for not only keeping students challenged, but people like me as well!
Good assumption, I just used the blue square is a little over 2.5 so nearest while number fitting scale being 3 and working through 😅yours is a much better assumption and much cooler too
I’d also assume the other unstated (but visually implied) given was that the arc intersected exactly at the lower left corner of the pink square. There’s nothing that says it is drawn to scale, but I don’t see a way to solve it without that implied corner contact variable. Good stuff.
Tried solving it but without that it's impossible. I saw that it was probably what I was missing but given it wasn't stated in the question you can't assume it's a fact.
This is also how I would approach this problem to begin with, how do you scale purple and blue square so that the third, pink square, will touch both the semicircle and align with top of the blue one? Purple and blue depend on each other (otherwise they either aren't squares, or don't add up to 5 base), so there is only one degree of freedom, then for each pair the pink square is implied and either accepts or rejects the solution.
Ah I see. The entire time I was wondering how it even makes sense to find a unique solution, given that you can draw the other 2 squares for any blue square, but with that restriction that doesn't really hold.
@@chaoticsquidno it's Def solveable without the circle. We know it's Fibonacci sequence. Which means we can run that sequence with a base dummy variable adding up each time and dividing that by five. The dummy variable represents the edge of orange square, and fibonnaci sequence dictates it'll repeat five times by now.
Thank you so much for the great content! As one who works as a math teacher, your content has been a huge inspiration on how to make challenging and fun puzzles!
Love your videos, doing these things with you are one of my favorite activities. Please take care of your own health and don't overdue with the videos and or any other job. Love you.
I love this channel. Would love to see a good explainer/refresher on exactly how integrals are solved, particularly when doing u substitution with going from dx to du. 😊
I never comment. Never subscribe. But you are crushing it. I save all of the problems that involve basic algebra geometry and algebra 2 concepts for my high school students. Andy Math out here differentiating instruction for me. God bless you and your family
You got as much views as your subscriber count in just 20h, wow ! This month has made your channel so viral: you've got your 2 most viewed video just this months. How insane ! Congratulations ! 🎉 Keep up the good work like that! 👍
Seeing this video reminded of my college days and learning of a square with negative dimensions. I think veritisium made a video about real life shapes that exist as the number i. Great content! Keep it up brother.
I have an exam today, and they ask a lot of area type geometry questions, I have been following you for a long time, if I get atleast one question that have concepts that you used, all Credit goes to you❤
I understand the process as soon as i see the problem. Math is very interesting, exciting and challenge. I love to go back in time and wanna challenge these math problems again😢
Wow, amazing how these can be solved, when at a first glance it seems impossible! Love watching these to brush up on my math skills👍 Trigonometry is my favourite!👍
With math problems like this a lot of the time they're not to scale, so it's important to check, but it's satisfying that the solution to this one actually is what it looks like.
Learned something new with your way of solving it. I managed to solve it but I assumed the smaller triangle intersect was right at the middle - Which I think it’s not a given so I’m considering my process luck 😅
Fibonacci and Generalization - Building on your process, paying close attention to the triangle which is the sum of two smaller ones, with specific ratio: We have x. Next, we have y=x+x=2x. Next, we have x+y=2x+x=3x. Next, we have x+2y=3x+2x=5x. This is the Fibonacci sequence where each term is multiplied by x. The first, same value as second, term is missing (we have 1, 2, 3, and 5, instead of 1, 1, 2, 3, and 5 - which correspond to the "bite" missing from the "complete" rectangle). using s for side lengths and a for areas, each followed by 1-3 for smallest to largest squares. Let's call the 4th term: z. specifically: z=5x. so: s1=z/5, s2=2z/5, s3=3z/5. Squaring for area: a1=z²/25, a2=4z²/25, a3=9z²/25. Summing: Total area = 14z²/25. In your example, z=5, so the total area = 14*5²/25=14. For z=6, for example, total area would be 14*6²/25=20.16. For z=10, twice the 5, the result should be quadrupled: 14*10²/25=56 - and it is.
An alternative way to solve this problem:trace a line beetwen the center of the semicircle and the point where the semicircle intersect the lower left corner of the smaalest square and apply the pitagorean theorem în the right triangle.
I did it a different way, label lengths of the squares from largest to smallest as a,b,c. Then we can create a set of equations a+b = 5 (1) b+c = a (2) To get a third equation we can take the point where the corner a is on the semicircle and use pythagoras, noting that the radius is r = 2.5: b^2 + (2.5 - c-a)^2 = 2.5^2 (3) add together (1) and (2) to get a+c = 5 + a - 2b = 5 + (a+b) - 3b = 10 - 3b (4) substitute (4) into (3) to get b^2 +(3b-7.5)^2 = 2.5^2, ==> 10b^2 - 45b + 50 = 0, ==> (2b - 5)(b - 2) = 0 ==> b = 2, 2.5 if b is 2.5 then a = 2.5 and c = 0 so total area is 12.5 (trivial solution) , and for b = 2, we get a = 3 and c = 1 so total area is 14.
Nice problem and nice resolution, bro! I've worked out the second equation by another triangle: the x²+y²=5² and used the the first equation squared as y²=(5-2x)².
Completely forgot about that right angle theorem; there are just so many from Geometry to remember .. I kept thinking about trying to use Pythagorean theorem on the x and y blocks to find the radius of that semi-circle..
I solved using the equation of the circle for 3 points like one of the other video you showed, you can declare 2 variables hx and Xx and you can write a system with 4 incognita and 4 equations solving for hx and Xx you get the same result but in a less elegant fashion
i did this using the Pythagoras formula. you know the center of the circle is 2.5 from the edge. you can draw a triangle that goes from the center of the circle to intersection of the circle and the 2 smaller boxes, then down perpendicular to the base of the semi circle. this has sides 2.5 (hypotenuse is a radius of the circle), y and 2.5-y+x. we can substitute x = 5-2y into that last side then the side lengths into Pythagoras formula to give us a quadratic in y. solve that to get y = 2 or y = 2.5 giving x = 1 or x = 0 (which we can discard) and finish up getting the areas.
I would like to know which software u use to make these videos (the software in which u teach) cz I wanna start teaching maths after my exams to my juniors through internet
I defined x as the length of a side of the smallest square like you did. Then I found ways to express the sides of the other squares with using x as the only variable: pink edge = x purple edge = 2.5-0.5x blue edge = 2.5+0.5x Then I put a right triangle between the bottom left corner of the smallest sqaure, the center point of the half circle and somewhere on the base line directly underneath that bottom left corner of the smallest square. The hypothenuse of that triangle would be identical to the radius of the half circle which is 2.5 and the other sides would be 1.5x and 2.5-0.5x (the purple edge). Using the pythagorean theorem I found x (the pink edge) to be 1 and substituting that into the above I found the purple and blue edges to be 2 and 3 respectively. 1²+2²+3²=1+4+9=14
HOW EXCITING🔥🔥🔥🔥🔥
Me and all my homies when Andy Math say HOW EXCITING🎉🎉🎉🎉🎉🎉🎉🎉🎉
🗣️🔥
Keep it at 777 likes
I’ve never seen someone so excited to solve the area of shapes
"how exciting" 3:55 love his constant excitement every video hahahah
Am I John Cena ni-
-ce friend of mine 😁😁
Well it will apply in shapes with a 90 degree triangle ofc. Squares and rectangles sure, but not trapezoids or kites and such (at least not all of them
I can't remember ever learning that an inscribed triangle along the diameter is a right triangle, but it makes sense. That's the conceptual step I was missing.
Never heard of Thales theorem?
@@Zieki99 Not that I can recall, but highschool was more than a decade ago and I don't use geometry in my day-to-day job. Again, it's just something I can't remember ever being covered, not that we didn't cover it.
Separate it to 2 isosceles triangles from the center, and apply all angles sum to 180 you get α+β=90
Shut up nerd
@@Zieki99I thought it was circle theorems
This guy is such a G. He's genuinely excited to just do geometry all day, and in such a simple and zen way we can follow.
The last time I needed to solve problems like this was around 15 years ago, but i still come here and try to solve these once in a while. The way you teach and explain is so good! Kudos for not only keeping students challenged, but people like me as well!
Pretty much same here. Im gonna start pausing at the start to try an do em myself. Hoping it'll keep my mind sharp!
Gonna be honest I just assumed they had areas of 1,4 and 9 because of the Fibonacci sequence
same
Good assumption, I just used the blue square is a little over 2.5 so nearest while number fitting scale being 3 and working through 😅yours is a much better assumption and much cooler too
Correct but you still need to prove it...
its an exponential sequece, not the fibonacci sequence... the fibonnaci sequece goes 1,1,2,3,5,8,13....
I’d also assume the other unstated (but visually implied) given was that the arc intersected exactly at the lower left corner of the pink square. There’s nothing that says it is drawn to scale, but I don’t see a way to solve it without that implied corner contact variable.
Good stuff.
Tried solving it but without that it's impossible. I saw that it was probably what I was missing but given it wasn't stated in the question you can't assume it's a fact.
This is also how I would approach this problem to begin with, how do you scale purple and blue square so that the third, pink square, will touch both the semicircle and align with top of the blue one? Purple and blue depend on each other (otherwise they either aren't squares, or don't add up to 5 base), so there is only one degree of freedom, then for each pair the pink square is implied and either accepts or rejects the solution.
Ah I see. The entire time I was wondering how it even makes sense to find a unique solution, given that you can draw the other 2 squares for any blue square, but with that restriction that doesn't really hold.
@@chaoticsquidno it's Def solveable without the circle.
We know it's Fibonacci sequence. Which means we can run that sequence with a base dummy variable adding up each time and dividing that by five. The dummy variable represents the edge of orange square, and fibonnaci sequence dictates it'll repeat five times by now.
Thank you so much for the great content!
As one who works as a math teacher, your content has been a huge inspiration on how to make challenging and fun puzzles!
Love your videos, doing these things with you are one of my favorite activities. Please take care of your own health and don't overdue with the videos and or any other job. Love you.
I like the way you solve problems. Quicker and much more exciting than the other youtubers.
Wish you will reach a million subscriber this year 😊
Your videos really helping me for my Olympiads =)
I cant believe this channel does not have more subscribers! Im am so glad i found you in my algorithm
I like that you explain how to solve the problem very succinctly and clearly.
love all you great videos Andy! thank you very much! :)
I can only be gay for Andy
Wtf man?!? He is just doing maths.
@@user-io1fq5jv1f some people cannot control themselves I guess 😂 desperate peeps really
Mind blowing! absolutely loved it.
I really love your videos! they are fun to watch
Who made bro so high and mighty in mathematics 😭
I love watching these. I'm hoping to remember some of it when I need it later!
You are just brilliant at explaining this stuff!
Seeing someone solve things like this perfectly is so satisfying 😭
I love how well made the puzzle is; so simple yet so many straightforward steps to solve it. Would buy a book full of these
I love this channel. Would love to see a good explainer/refresher on exactly how integrals are solved, particularly when doing u substitution with going from dx to du. 😊
I never comment. Never subscribe. But you are crushing it. I save all of the problems that involve basic algebra geometry and algebra 2 concepts for my high school students.
Andy Math out here differentiating instruction for me. God bless you and your family
Beautiful! 🔥
Wish my math lessons were this intriguing when I was a youngster !
You got as much views as your subscriber count in just 20h, wow ! This month has made your channel so viral: you've got your 2 most viewed video just this months. How insane !
Congratulations ! 🎉
Keep up the good work like that! 👍
Very simple and straightforward explanation 👌
I remembered how to form that first right triangle but didn't figure out the step to form the similar similar smaller ones. Cool stuff!
I’m a healthcare professional and your videos fill the void of math in my field.
Merci pour ces vidéos, je suis impressionné par la facilité dont résout ces problèmes
I like that you always go for geometry problems that can be solved by high school level mathematics yet are still challenging.
I’m proud that I found you before you reached a million subs (which I know for sure will happen!)
Seeing this video reminded of my college days and learning of a square with negative dimensions.
I think veritisium made a video about real life shapes that exist as the number i.
Great content! Keep it up brother.
This guy helps me with geo better than any tutor
I have an exam today, and they ask a lot of area type geometry questions, I have been following you for a long time, if I get atleast one question that have concepts that you used, all Credit goes to you❤
Very nicely done!
Another video from my favorite math teacher youtuber
Im gonna have test from plane geometry soon, this is actually gonns be pretty helpful (we do these kinds of exercises) 🔥🔥
Fun fact, although is only a small sample, those squares apear in representations of the Fibonacci sequence.
I love how clear his explanation is. No unnecessary talking so that even a non-native speaker who always sucked at math can follow easily!
This is an exiting classic!
It’s been 2 plus decades doing this and enjoyed. I had to pause to get my memory going 😂
Hola andy, me encantan tus videos, siempre me sorprende la forma tan sencilla en la que solucionas los problemas. Saludos desde Colombia ^^
¡Gracias!
Another banger from Andy
I'm starting to really like your channel
Thank you for revising all concepts sir❤
Such an elegant solution with whole numbers.
My lord. That was insane dude
Clear, clean and elegant solution.
Although I would improve a little the graphic animation, still it's an excellent video.
Big like ❤👍
You're right, that WAS a fun one :D
Dudes a natural
I understand the process as soon as i see the problem. Math is very interesting, exciting and challenge. I love to go back in time and wanna challenge these math problems again😢
Its cool that i could just try guessing these squares and still get it right
Wow, amazing how these can be solved, when at a first glance it seems impossible!
Love watching these to brush up on my math skills👍 Trigonometry is my favourite!👍
It’s fun when you can approximately do it by eye and assumption of whole numbers, but the correct algebraic method is interesting to follow along
At each equation found you can feel that it makes he happier 😂
I forgot how satisfying it was to solve geometry equations! the same as like figuring out a puzzle
Idk know why but i love to watch this
Excitingly waiting for next video😊❤
This is appeared in my recommendations and is the best recommendation that CZcams gave me today.
Truly an exciting answer
I like your funny words, magic man
With math problems like this a lot of the time they're not to scale, so it's important to check, but it's satisfying that the solution to this one actually is what it looks like.
Outstanding.
Learned something new with your way of solving it. I managed to solve it but I assumed the smaller triangle intersect was right at the middle - Which I think it’s not a given so I’m considering my process luck 😅
Interesting… at a glance, I wondered if those were the proportions, but assumed it wouldn't be so simple!
Fibonacci and Generalization -
Building on your process, paying close attention to the triangle which is the sum of two smaller ones, with specific ratio:
We have x. Next, we have y=x+x=2x. Next, we have x+y=2x+x=3x. Next, we have x+2y=3x+2x=5x.
This is the Fibonacci sequence where each term is multiplied by x.
The first, same value as second, term is missing (we have 1, 2, 3, and 5, instead of 1, 1, 2, 3, and 5 - which correspond to the "bite" missing from the "complete" rectangle).
using s for side lengths and a for areas, each followed by 1-3 for smallest to largest squares.
Let's call the 4th term: z. specifically:
z=5x. so:
s1=z/5, s2=2z/5, s3=3z/5. Squaring for area:
a1=z²/25, a2=4z²/25, a3=9z²/25. Summing:
Total area = 14z²/25.
In your example, z=5, so the total area = 14*5²/25=14.
For z=6, for example, total area would be 14*6²/25=20.16.
For z=10, twice the 5, the result should be quadrupled: 14*10²/25=56 - and it is.
I wouldn't have thought to use a similar triangle proportion. Obscure methods are exciting.
I loved this.
you make it look so simple!
I love it.. thanks for the good videos.. you are great..👍👍
An alternative way to solve this problem:trace a line beetwen the center of the semicircle and the point where the semicircle intersect the lower left corner of the smaalest square and apply the pitagorean theorem în the right triangle.
I did it a different way, label lengths of the squares from largest to smallest as a,b,c. Then we can create a set of equations
a+b = 5 (1)
b+c = a (2)
To get a third equation we can take the point where the corner a is on the semicircle and use pythagoras, noting that the radius is r = 2.5:
b^2 + (2.5 - c-a)^2 = 2.5^2 (3)
add together (1) and (2) to get
a+c = 5 + a - 2b = 5 + (a+b) - 3b = 10 - 3b (4)
substitute (4) into (3) to get
b^2 +(3b-7.5)^2 = 2.5^2,
==> 10b^2 - 45b + 50 = 0,
==> (2b - 5)(b - 2) = 0
==> b = 2, 2.5
if b is 2.5 then a = 2.5 and c = 0 so total area is 12.5 (trivial solution) , and for b = 2, we get a = 3 and c = 1 so total area is 14.
I solved it with the same approach!
Best video ever watched after waking up
Nice problem and nice resolution, bro! I've worked out the second equation by another triangle: the x²+y²=5² and used the the first equation squared as y²=(5-2x)².
Completely forgot about that right angle theorem; there are just so many from Geometry to remember .. I kept thinking about trying to use Pythagorean theorem on the x and y blocks to find the radius of that semi-circle..
I never thought I could be that much interested in maths 😮
I love it!
The fact you dont even have 100k subs should be a crime, and thank you on another hreat video
I solved using the equation of the circle for 3 points like one of the other video you showed, you can declare 2 variables hx and Xx and you can write a system with 4 incognita and 4 equations solving for hx and Xx you get the same result but in a less elegant fashion
Pretty fun one!
Brilliant!
i did this using the Pythagoras formula. you know the center of the circle is 2.5 from the edge. you can draw a triangle that goes from the center of the circle to intersection of the circle and the 2 smaller boxes, then down perpendicular to the base of the semi circle. this has sides 2.5 (hypotenuse is a radius of the circle), y and 2.5-y+x. we can substitute x = 5-2y into that last side then the side lengths into Pythagoras formula to give us a quadratic in y. solve that to get y = 2 or y = 2.5 giving x = 1 or x = 0 (which we can discard) and finish up getting the areas.
What do you use for the whiteboard? I love it
I would like to know which software u use to make these videos (the software in which u teach) cz I wanna start teaching maths after my exams to my juniors through internet
This is a good one.
Ngl this shit was so fun to watch I ❤ maf
WE GETTING OUT OF MATH CLASS WITH THIS ONE 🙏🙏🙏🙏😭😭😭🌛🔥🔥🔥
I defined x as the length of a side of the smallest square like you did.
Then I found ways to express the sides of the other squares with using x as the only variable:
pink edge = x
purple edge = 2.5-0.5x
blue edge = 2.5+0.5x
Then I put a right triangle between the bottom left corner of the smallest sqaure, the center point of the half circle and somewhere on the base line directly underneath that bottom left corner of the smallest square. The hypothenuse of that triangle would be identical to the radius of the half circle which is 2.5 and the other sides would be 1.5x and 2.5-0.5x (the purple edge). Using the pythagorean theorem I found x (the pink edge) to be 1 and substituting that into the above I found the purple and blue edges to be 2 and 3 respectively. 1²+2²+3²=1+4+9=14
i love him so much
He never fails to disappoint 🔥🤑👌
Found 14 myself. Amazing problem, by the way.
Cool problem! I ended up with 14 by setting (2.5-y+x)^2 + y^2 = 2.5^2 based on where the semicircle overlaps with the pink square’s corner.
Hi, what's the software you're using to write the math?
This is so frickin cool
Отлично объясняешь, спасибо 😊 thanx
This shows how logical reasoning gets you the correct answer very quickly, but proving that it is correct is a long and confusing path.
You make math fun
Hey Andy what are your qualifications?
this is my daily dose of ASMR