I may have a PhD but I'm also failing 4th grade math 💀😭! Twitter geometry problem

The square below is made up of four small squares. Can you shade half of it so that the unshaded part is also a square? This math question is from Twitter, aka X, / 1780732556989591721
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#math #algebra #mathbasics

[@bprpmathbasics]

Try this next: kzbin.info/www/bejne/jnWup3WgqN-jnc0si=TK-h3GqdlvkJh-Bc

[@anuragguptamr.i.i.t.2329]

Sir, she already had got the solution from MindYourDecisions... kzbin.info/www/bejne/inPCkIKdaL2hiJosi=hLtoCjFH4RjmyQ8F

[@Scudmaster11]

You can just shade 2 opposite corners

[@proxima4zo6g89]

The person was probably overthinking this problem and end up short-circuiting herself

[@Stormer13]

I honestly can't tell you how often that happens in my lab, and we just laugh about it after we realize we're trying to over-engineer things.

[@iout]

There’s probably some overthinking, but I reckon there’s also a fixation with the grid going on. The gridlines trick you into focusing on solutions that also align with the grid. For me it took a few tries before I was able to shake the fixation and realize I was allowed to rotate it.

[@neilgerace355]

The small square can be positioned anywhere within the big one, so there is an infinite number of solutions.

[@robertvelasquez823]

Because of this comment, I got the idea of making a diamond of equal length per line, i.e. making a diamond shaped square to have the answer make sense.

[@Ninja20704]

But the problem is that you need to draw a length that is exactly sqrt(2). The only way i can that being achievable is the using the grid lines which is the solution in the video. I can’t see any other way which would let you freely position/orientate the square.

[@abhiswarakumbhare5468]

​@@Ninja20704 Yes, but this seems easier than the one I thought of

[@tommyb6611]

But it's very difficult to prove half of it (or very very close) in 99.9999% of the positions. Only a few you can prove it's actually half Or very close) *very close is defined by the size of the actual square used, because to perfectly represent 1.41 is impossible when the line of the pen/pencil used to define igh represent more than 0.1% on it's own.

[@neilgerace355]

@@Ninja20704 Constructing a line segment that is sqrt (2) times the length of another line segment can be done with a compass and straight edge.

[@sapincher]

*casually stops trying to figure how to measure out 1.414* oh yeah that's good!

[@JayTemple]

That is absolutely constructible, especially if you're given the lines in the picture. (1) Use a compass to measure the distance from a "main" corner to the center." (2) Measure that distance away from one corner in both directions. (3) Construct perpendiculars to each side from those new endpoints. The perpendiculars will meet at a spot that forms a square whose sides are all sqrt(2). (In contrast, ISTR that the cube root of 2 is not constructible.)

[@Patrik6920]

..its a 4th grade q .. if u understand the concept .. not a test of ur ability to draw a line... if a teacher would fail anyone on such grounds ... well maby he/she shouldent be a teacher...

[@chitlitlah]

Exactly the way I was thinking of doing it.

[@ingiford175]

You can also draw a circle using an edge and the center point of the square, the intersection to the square will give you root (2), provided the sides of the little square of 1. Make perpendiculars at each of the intersection and that square is exactly half the area of the original square.

[@rickhole]

If you want the 1/2 area square centered, inscribe a circle from the center tangent to the sides of the outer square. Draw the diagonals of the outer square. Mark the four intersections of the circle and the diagonals. Connect those four points for a square. Shade the area between the new square and the outer square. Done. Note that this square could also be obtained by taking the square on the diagonals that John demonstrates and rotate it 45 degrees. You could rotate that square to any angle (infinite number of solutions) or translate it anywhere and any rotation that fits into the outer square. See JayTemple for another great construction which puts the solution square in a corner.

[@tobybartels8426]

While this is probably what they wanted when they set the question, another method is to draw a circle centred at one of the vertices of the big square with a radius leading to an adjacent vertex of the big square, then draw a line to the opposite vertex of the big square to see where it intersects the circle, and make that point the opposite vertex of your half-size square. (If you see what I mean; this would be better with a drawing.)

[@richardhole8429]

yes! That gives a proper construction and gives an internal square with side a/sqrt(2). I was settling for an approximation. Thank you!

[@tobybartels8426]

Dang, made a constructive edit and lost my heart. 😞

[@Patrik6920]

@@tobybartels8426 ..ooh dont be sad .. ive heard a heart can be reconstructed with a couple circles and tangent lines...

[@pa28cfi]

My first thought was to draw a square connecting the center points of the 4 smaller squares, and shade the outside portion between the large square and the centered smaller square. Then I realized that wouldn't work since halving the side length, reduces the area by 3/4.

[@romajimamulo]

I thought the shaded area also had to be a square and I screwed myself up

[@kpingvin]

If I had a Phd in a STEM subject I wouldn't tell anyone that I couldn't solve this.

[@overlord3481]

PhD doesn't mean you are good at that subject.

[@juliavixen176]

It might be clickbait engagement for Twitter. The only people still using Twitter these days are farming it for outrage.

[@omerkaya545]

Just cut each square diagonally into a half. Then put them together and boom, you got a empty square in the middle.

[@spacebar9733]

OHHHHH LOL thank you !! 🙏🏾

[@angellance17]

No way she has a PhD and couldn't figure this one out.

[@justcommenting5117]

I went into a similar path, but the sides of square made of the unshaded area were paralel to the other squares (or perpendicular depending on the sides you're comparing)

[@philc2729]

Yes, there are more than one solution. You can also block out sqrt(2) from any side and shade outside that region eventually creating another square

[@Dexaan]

I assigned the squares sides of length 1, drew a triangle that covered half the large square, got the area of that, then drew a square with that area inside.

[@ingiford175]

You can also draw a circle using an edge and the center point of the square, the intersection to the square will give you root (2), provided the sides of the little square of 1. Make perpendiculars at each of the intersection and that square is exactly half the area of the original square.

[@descuddlebat]

First thought was using a circle to copy a diagonal since it's the right size, next thought was to use the diagonals directly like this

[@CcReap3r]

All I got was using one of the squares as a base 1x1 then marking a point x distance off both points where the square ends on the side. The areas created by where those two points would intersect inside the square would be 1 times X, 1 times X and X times X and they would all equal 1 unit of area. 1=x^2+2x -> x^2+2x-1 ->quadratic formula -> √2-1. So just mark the offset and shade around that corner....probably lol.

[@craighyattusa]

I might not have heard the rules of the problem, but my first thought was shade below the diagonal from UL to LR corner. The square is then divided into two equal area triangles.

[@athormaximoff4634]

I was so fixated on making a square with sides equal to √2 in the *middle* that I forgot yoy could just do diagonals 😂😂

[@aninterestinusername]

This was probably the first video I’ve seen from this channel where I was able to figure out the answer right away lol

[@mybloodyvacuum]

same

[@newidentity292]

I guess "imagination" and "creativity" are much important that basic knowledge

[@givikap120]

This is because of the meaning of word "half" in this context If it was changed to "shade half of the square surface" - it's suddenly becomes much easier because now you know that square is not consisting of integral smaller squares

[@tonyennis1787]

if the small squares are 1x1 then the distance between the midpoints of the big edged are sqrt(2) long. So connecting all these intersections gives a square-on-point with side lengths sqrt(2). The area of this square is sqrt(2)*sqrt(2) = 2. The area of the original square is 4. Then shared outside the square we just made. QED.

[@joshuaanoruo973]

I got that the length of side of the big square is root 2 times the length of side of the small square. I then realised that the diagonal length of a square are root 2 times side length so I rotated the small square in such a way that it's diagonals were parallel to the sides of the big square

[@LostShamen]

Shade each smaller squares to make right angles

[@Nikioko]

I would have done it the same way. This is basically the visual proof of the diagonal of a square being a√2.

[@Trigun_arcx]

D’OH!!😂

[@jdotoz]

1) Construct a square of half the area of the big square. 2) Place it anywhere in the big square. 3) Shade the area outside the square you built but inside the big square.

[@natewoods4566]

It says "can you", what if the correct answer is "no"?

[@zdkshinxi]

I would just use a ruler.

[@tomasbeltran04050]

Find (0, l/sqrt(2)) as a point in a side on ðe original square, where l is ðe side of ðe original square. Draw a line of l/sqrt(2) lengþ and ðen anoðer one from its endpoint until ðe furðest side.

[@okaro6595]

There has to be some additional rule like that one cannot use a ruler to measure things.

[@johnbollenbacher6715]

In other words, using only a compass and protractor.😊

[@richardhole8429]

Oh, I was overcomplicating it. I was leaning to ignore the grid and draw a square in the middle such that each side is of length x / sqrt(y) where y is the side length of the outside square. My solution works but cannot be constructed precisely.

[@theonewhoasked513]

Making a square donut is gonna be harder than this 😂

[@someshta]

I haven't watched this, but the solution is obvious.

[@firstptr3and10_]

My feelings are hurt 😂

[@abinaya3910]

leave a square ot in the centre of length a/√2 ?

[@BenHyle]

That's a lot of work compared to the method shown

[@xanderlastname3281]

I blame the lines I assumed that the unshaded part had to fit within the pre-existing squares (in which case its impossible, as no comination of 2 squares results in a square) Had i known that the half-sized square could be wibbly wobbly bibble bobble across wherever the hell it wants id have gotten this within the minute with the 'draw diagonals to make a square rotated 45 degrees' Anyway cool

[@haabyalexis1157]

14 seconds and no views...these kind of comments really show how humor has fallen off Note thet i didnt realize the video was new when I clicked on it..i watched it and i enjoyed it! Keep up the good work :)

[@jeanmouloud9795]

I think that's it was not how he think about the problem. Personnaly i understand it that the shade part and the not shade part has to be square, because it said "also a square".

[@Misteribel]

Didn't you publish this already a few days ago? Trivial, but still fun idea.

[@DerekGreen15]

I think that was MindYourDecisions

[@godhell8039]

Hey! I solved this! Now I want a doctorate too! 😂

[@to2podemosaprender630]

I wa.thunking making a square with 1.4242 side! So we shade the remaining L shape part!

[@chris.y.l.o]

Was easy af I feel like a genius

[@davidcooke8005]

Just turn the paper over and shade the back half.

[@Ruija27]

Connect the four midpoints of the big square. Now you have four triangles in the corners and a square region at 45 degrees relative to the bigger one. Shade the triangles and you're done. Or you can be cheeky, and just draw a smaller square inside the big one, and say its side length is root(2).

[@richardhole8429]

Yes, except the triangles are isosceles, not equilateral, but that is irrelevant to your solution. Just call them triangles and you are good to go.

[@johnbollenbacher6715]

There are many ways to shade this if you’re not restricted on the shape of what you shade. You found one. My guess is that the teacher intended to ask “can you shade half of each square…“ Then your solution is probably the only one available. Or maybe it was implicit that you can only use a compass and projector.

[@johnbollenbacher6715]

Can we just agree that it’s not a well formed problem?

[@MuffinsAPlenty]

@@johnbollenbacher6715 It's a well-formed problem, though it has multiple correct answers. Yes, the one given in this video is probably the intended solution, and it's also probably the only one you can draw with absolute certainty. But just because a problem has multiple solutions does not mean it's ill-posed.

[@johnbollenbacher6715]

@@MuffinsAPlenty I guess i I would still argue that it’s ill-posed if the student is 11 years old. But maybe that’s not what it’s meant by fourth grade. But I keep hearing how kids these days are smarter than we were. :-)

[@alimfuzzy]

Grade school (and basic learning in general) should be about learning the basics and not trying to trick them as part of regular curriculum. It discourages them from learning if they can't do it. Instead they should have challenge tasks that don't go towards final marks that help them think outside the box and only for those who want to do it. School is meant to be about encouragement and foundational learning, not boosting the question writers ego for making tricky puzzles.

[@LINX009XBL]

How do you know this isn't a challenge question that was asked for? There isn't any indication in the post that it is a regular question that students are expected to know. As for the question itself, whether it is a challenge question or not, this question is a good way to help students find innovative ways to think about a problem. The fact that there are so many possible ways to solve this problem that range from no math at all (simply understanding that a square can be cut in half diagonally making two triangles) and going as complex as you want to find a solution helps someone think in a way they may not already think. When I saw it, I thought of triangles as he demonstrated, but some might immediately go to math since the post identified it as a math question.

[@martineyles]

The lines throw people off, but the intent of the lines is to help you by giving the midpoints of the sides of the big square.

[@alimfuzzy]

@LINX009XBL I can't be sure but my point remains, because in general that's how schools have worked for decades. I was going by the usage of the word 'failing' to assume this was a regular graded question.

[@alimfuzzy]

@LINX009XBL as for your second point. It's true outside the box thinking is good, but as I said there are many who get discouraged from school because they can't do "trick" questions. Western schools go by the everyone learns at one pace or gets left behind, it's a product of standardised testing and bad teaching methods. In the best schools in the world, they teach to learn and don't use trick questions test aptitude. There are actually better ways to teach outside the box thinking and that is to actually teach abstract methodology practices specifically and then apply it to different subjects. At which point it encourages students who have mastered the foundations to ho further without hindering those who are not at the same level.

[@juliavixen176]

This thing was setup as engagement bait on Twitter, and everyone keeps falling for it.

[@bRiMaTiOn]

Make a square with 50% of the total area then. Thank you everyone

[@88kgs]

Super👍

[@AllanPoeLover]

那種智商很難令人相信是博士學位的人

[@sydwelglobal1439]

It’s a poorly written question! It should have said, “can you shade half of the total combined area of the squares”! People who think they are smart sometimes lack basic common sense!😂

[@theonewhoasked513]

Bruh I solved it without clicking on the video 😂

[@wisteria3032]

this is quite interesting I think. take me. I like math. never studied it seriously but I'm good at it and grasp the concepts quickly. My SO hates math and doesn't remember anything except the basis. He also severely underestimates himself because of shitty teachers and thinks that since he doesn't immediately get new concepts it means he is stupid (hint: he's not). Our reactions to this were completely opposite. First thing that came to mind for me was: let's say the small square had a side of 1. Big square has side of 2, area of 4. to get half the area I need a square with the area of 2, which means a side of √2 Now where do I easily find the √2? obviously the small square diagonal. So I point a compass in the upper right corner, open it to get the measurement of the diagonal, sign it on the sides I already have, finish constructing the new square and cancel the rest. He looked hard at it for 30 seconds and said "can't I just shade half of each square diagonally and make a new square in the centre? maybe it's a stupid idea" I hadn't even thought about it. And when I told him what my solution was he said "yours is way more elegant than mine". I couldn't believe my ears, had to explain to him it was the other way around. He was "but mine can't be better than yours, it's too simple". And that's how shitty teachers ruin a person.

[@richardhole8429]

Responding to the comment that rotating the square is not allowed by the problem, the problem does not prohibit a rotated solution. There are an infinite number of solutions and you must simply find one of them.

[@comdo777]

asnwer=15cm

[@e.m.p2261]

I'm teaching math

[@absolutezero9874]

Don’t say you didn’t see my question

[@paulfillingham4778]

There is a simple solution

[@lavatrex]

can’t u just make a diagonal square pretty simply?

[@tommyb6611]

If that user has indeed a phd, shows the failure of the educational system. To be allowed phd, candidate should have min IQ130

[@juliavixen176]

Or it's engagement bait for Twitter.

[@richardhole8429]

Let's be kind. I have been an engineer for more than 50 years and did not see the simple solution presented here. I did see a solution somewhat more complex. Many, including our PhD friend fell for the trap in this problem of thinking that the shading must be of the four inner squares, not realizing they can be ignored.

[@fazom1707]

PhD was never a measure of intelligence by any means, nor was it meant to be. It's also possible this person has a PhD in an area completely unrelated to mathematics, not to mention it wouldn't make sense to demand someone with a PhD be skilled in mathematical reasoning to be qualified for an entirely different area.

[@fazom1707]

Academic degrees shouldn't be confused with high intelligence, nor should one be necessarily a prerequisite for the other, especially in such a specific way. Quite a few fields of knowledge just don't demand *that* many critical problem solving abilities (130 IQ) and logical thinking of the like for one to be reasonably proficient in, take humanities for instance.

[@juliavixen176]

IQ isn't real.

[@GaMeSpaCe_-vh2zv]

The fact that people can have a degree or something but still fail in these things because they cannot think out of the box probably people who play those brain games would have solved this because it actually helps to make your out of the box thinking better tho I didn't need any it was just an easy question but don't worry guys it's not that big problem if you still worry then you can fix it

[@overlord3481]

Phd does not mean intelligence.

[@juliavixen176]

The only people still using Twitter are posting enragement bait to generate revenue, and you feel for it.

[@MuffinsAPlenty]

And not being able to figure out a single problem also doesn't mean lack of intelligence.

[@deep_meaning1]

🇳🇬🇳🇬🇳🇬

[@mindustrymaster]

ez

[@absolutezero9874]

Continue ignoring 👍🏼👍🏼

[@Phyrre56]

The problem with this question is that it is not math. It's a logic puzzle or a brain teaser. The solution requires a leap of faith that the grid lines are misleading and should be ignored. That's a fine skill to teach and test but it's not math.

[@richardhole8429]

I would differ with you. It is indeed math.

[@dh8203]

It's geometry which is usually taught as a part of the math curriculum.

[@ZipplyZane]

A whole lot of geometric proofs involve adding new line segments. It takes something that can seem very complicated and turn them into something rather easy. I'm horrible at those types of geometric proofs, but I wonder if exposure to the concept as a kid would have helped. At the end of the day, what mathematicians actually do is creative problem solving. The rote stuff we learn in math classes isn't the actual mathematics, but the tools that allow us to do math.

[@ZipplyZane]

The proper geometric version, BTW, would go something like this. 1. Label the 9 intersection points left-to-right, then top to bottom, creating a set like this: ABC DEF GHJ 2. Construct line segments BF, FH, HD, and DB to create square BFHD. 3. Shade in all areas outside square BFHD but inside square ACJG

[@someonespadre]

Hint: just ignore this idiocy, don’t need more videos about it. I personally think the diagonal square answer is not responsive to the question.

[@richardhole8429]

I didn't see that obvious solution either, join the club. But why do you reject it? It is a square with half the area

[@LINX009XBL]

I don't understand the reasoning for the rejection either since it is a solution, not only that but one that requires little to no math to understand.

[@xinpingdonohoe3978]

So you are saying that the unshaded part is not a square?

[@someonespadre]

Nothing in the problem statement allows for rotating the square like that. The closest reasonable answer is shade opposite squares. There really isn’t an answer but that’s as close as one can get.

[@richardhole8429]

​​@@someonespadreIt also does NOT rule out a rotation. The definition of a square does not include that it be parallel to the axes, only that it's sides be equal and the angles be right angles.

[@CashewBestofNuts]

I can't find an answer for this. Can you make a video please? 🙏 ⁿx is what compared to xⁿ not an exponent it is a what? And what is the difference. ³x= vs x³=