AMASE: Close Packing

Posted on Tuesday, January 12th, 2021


[Mother and daughter cutting paper at the kitchen bar.]

Joanne: Alright on today's episode of Ask Me Anything: SCIENCE EDITION Mara has a question about one of her favourite things...SNOW! 

[Cut to Guelph Physics Logo]

[Cut back to kitchen]

Mara: I... was just wondering... why snowflakes... had six sides? 

Joanne: Good question! So, what is snow made up of?

Mara: Uhhhh... water.

Joanne: Water! And what is water made up of?

Mara: Molecules? 

Joanne: MOLECULES! And what is in each molecule of water?

Mara: \(H_2O\)? Two hydrogens and an oxygen? 

Joanne: Two Hydrogens and one Oxygen. Three atoms for every molecule. And those atoms arrange themselves in almost a triangle shape!

[Holding up 2 fingers on one hand and one on the other hand. Then moving fingers into a triangle] 

Now if you're trying to pack triangles together really efficiently so there' s no space in between what shape do we end up with?

Mara: Ummm.... let me try it out. 

Joanne: We're going to try it our with some triangle crackers! 

[Joanne lifts a plate of crackers.]

We've got some triangles, some circles, and some squares here. Let's make some space. Alright!

Let's take our triangle crackers and arrange them as efficiently as we can with as little space in between... So what have we got when we arrange our triangles?

[Mara counts the sides of the shape made with the crackers.]

Mara: A hexagon!

Joanne: The water molecules are like triangles and they arrange themselves efficiently in a hexagon shape with very little space in between. 

Alright what happens if we take our circles?

Ok what have we got? It's a nice pattern but is it as efficiently packed as the triangles?

Mara: No it's kind of a hexagon... but it looks more like a flower.

Joanne: It does kinda look like a flower and it's got a lot of spaces in between. They don't pack as well, these circles, right?

Mara: It looks like a honeycomb!

Joanne: Shall we put these ones together, the squares, and see what we get?

Squares go together pretty nicely too!

Ok so the shape determines how the objects pack together efficiently. And HOW efficiently they pack together meaning how little space there is left over in between.

So we can talk about that with two dimensional shapes we can also talk about it with three dimensional shapes.

[Joanne holds up a dice and a small ball.]

So do you want to do another experiment? 

Mara: SURE! 

Joanne: Alright! So we're going to fill containers with cubes and spheres and then we're going to see how much space is left over.

[Video transitions to same counter with a large measuring cup of green liquid, a cylindrical container of small balls and a square container of dice.]

Joanne: So we've got them all lined up.

Mara: And they're the same type so this is like a round container and these are balls and this is a square container and these are cubes.

Joanne: And they're both 32 fluid ounces. So we've got 32 fluid ounces of water. So which one do you want to do first and see how much you can get into that container?

Mara: Dice! Alright we're gonna see how much!

Joanne: Pour slowly.

Mara: greeeen water

[Mara pours liquid slowly into dice container.]

Joanne: Ok how much did you get in there?

Mara: Barely any. We started with four cups... and we now have 3 and a half cups.

Joanne: Ok and on this side we'll read it in millilitres 820 mL or so?

Mara: So we've done the dice! And now we are moving on to the balls. 

[Mara pours liquid into the ball container, the balls float a bit and Joanne holds them down.]

OH!!! And that took... almost two cups!

Joanne: Wow! 

Mara: Wow.

[Video cut to Mara and Joanne sitting back at the kitchen bar.]

Joanne: Ok! So! In our experiment we found that the cubes we could only pour in 175 mL into that container until it was full. But with the spheres there was a lot of empty space and we could pour 500 mL of water into that container to fill that empty space.

So the cubes fit much more efficiently than the spheres.

[Video frame of Joanne and Mara shrinks to show diagrams beside them of squares, circles and triangles packed together.]

Kinda like the squares pack more efficiently than the circles!

[Joanne and Mara fill the frame again.]

Mara: So! I know that circular crackers don't pack efficiently together but they're still my favourite to eat.

Joanne: There you have it. So thanks for watching today's episode of 

Ask Me Anything: Science Edition!

Enjoy the snow!

[Video transitions to white ground with a Royal City Science Logo, and bubbles around the edge of the screen as music plays.]

Royal City Science. Naturally Curious.


Ask Me Anything: SCIENCE EDITION is BACK for 2021!

Dr. Joanne O'Meara and junior scientist Mara are examining packing structures of solid shapes and how it relates to snowflakes!

Got a question for our team to answer? We're doing what we can here at Physics, University of Guelph to help out educators right now.

Do you or your students have fun science questions you'd like to explore? Hit us up on FB or IG and we'll throw together a fun video response for you!

Any grade level, any subject, the zanier the better!

We look forward to hearing from you!

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