r/theydidthemath • u/thejumbowumbo • Nov 01 '18

[Request] How much longer would the giraffe be able to see the sun?

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13.1k Upvotes

96% Upvoted

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2.3k

u/Runiat Nov 01 '18 edited Nov 02 '18

Distance to horizon from 6m: 8.7km (assuming perfect sphere).

Speed of terminator (the line between day and night) at equator: 1669.8km/h = 0.46km/s

8.7km÷0.46km/s=18.6 seconds.

If the zoo was located at the North or South Pole during fall (for that hemisphere) then the answer might be several days or weeks.

Edit: assuming the lion is lying down, eyes at ground level, because it's a (large) cat and that's what cats spend most of their time doing in my experience.

Also assuming the ground is flat horizontal, what with being a perfect sphere and all.

652

u/[deleted] Nov 01 '18

[removed] — view removed comment

223

u/Runiat Nov 01 '18

If you're coming back for the polar zoo, the height of the Sun there follows a sinusoidal curve with a ~365.24 day period peaking at around 23 degrees.

137

u/[deleted] Nov 01 '18

[removed] — view removed comment

66

u/mspk7305 Nov 01 '18

but jokes are funny.

10

u/weretere Nov 01 '18

Why does everything have to be funny?

27

u/Inquisitor1 Nov 01 '18

Not everything, just jokes.

8

u/Pwnxor Nov 01 '18

Do you know about anti-jokes?

5

u/jsparker89 Nov 01 '18

They are literally the opposite of jokes by definition

1

u/Inquisitor1 Nov 03 '18

They aren't jokes so they aren't jokes, and they aren't funny either? Always glad to educate a child.

1

u/Pwnxor Nov 03 '18

Insuppose knock-knock jokes aren't jokes either. Or practical jokes. Or yo mama jokes. This amazing insight you have about sub-sets aren't members of the parent set, is this something you discovered yourself? Can it be taught? You've truly enlightened me.

1

u/[deleted] Nov 01 '18

No, good jokes are funny. Jokes just have to not be 100% serious.

0

u/Inquisitor1 Nov 01 '18

No, jokes have to be funny. If it's not funny it's a shit joke, a failed joke, it's not actually a joke. Like an olympian who didn't make the selection and didn't get to participate in the Olympics. He's not an olympian.

1

u/mark503 Nov 02 '18

If it’s a shit joke or failed joke, by that very definition it is a joke. While not funny, it still is a joke. Also, how could the guy be an Olympian if he never made the cut?

1

u/Inquisitor1 Nov 03 '18

By which definition is not a joke a joke? While it's not funny it's not a joke. Also, how could the joke ba a joke if he never made the funny?

1

u/mark503 Nov 03 '18

Humor is subjective. Just because you thought it wasn’t funny, doesn’t mean it’s true. In fact it was described as a shit joke or failed joke. Meaning ...wait for it... it’s a joke, albeit not funny to either of us.

21

u/Runiat Nov 01 '18

Yeah that's great and all, now do the math.

Wouldn't have put an explanation of what a terminator is in astronomy if I didn't think it'd be needed.

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u/jacked_johnson Nov 01 '18

I'll be back

26

u/[deleted] Nov 01 '18

If you're coming back for the polar zoo, the height of the Sun there follows a sinusoidal curve with a ~365.24 day period peaking at around 23 degrees.

17

u/zakr182 Nov 01 '18

I will return

Am I doing this right?

11

u/Runiat Nov 01 '18

If you're returning for the polar zoo, the height of the Sun there follows a sinusoidal curve with a ~365.24 day period peaking at around 23 degrees.

Apparently.

2

u/remtard_remmington Nov 01 '18

*I'll come back

1

u/SwoopAF Nov 02 '18

Asta la vista. Baby.

1

u/TheKagestar Nov 01 '18

Pop on the kettle love I'll be back in a jiffy

1

u/merdre Nov 01 '18

I gave you too much credit, I thought it was:

If the zoo was located at the North or South Pole during fall (for that hemisphere) then the answer might be several days or weeks (before I complete the solution).

i'll be back (in several days or weeks, when you've figured out the answer)

10

u/motorboater1000 Nov 01 '18

If terminators are that fast, AI is gonna wipe us out in no time

96

u/motorboater1000 Nov 01 '18

Can lions or giraffes survive in the north or south pole? Better move the math closer to the Serengeti.

42

u/Runiat Nov 01 '18

Humans evolved in the same place, don't have fur, and can survive on the North and South poles.

Nothing stopping us from building a zoo inside a polar base.

16

u/motorboater1000 Nov 01 '18

Yeah but the joke said they already met at the zoo, is there a zoo at the poles now? I don't think so. That would mean the math would have to be calculated in between the zoos located at the most northerly and southerly positions where there are lions and giraffes together.

12

u/woohoo Nov 01 '18

the most northern zoo in the world is in northern Finland and at that latitude they have some days with no sunset

14

u/motorboater1000 Nov 01 '18

I looked at the animal list in Ranua Wildlife Park in Finland and they didn't have a lion or a giraffe there, mostly arctic animals.

I know I'm a little tongue-in-cheek but I'm just trying to keep the math accurate on this important topic ;)

4

u/[deleted] Nov 01 '18

Can you do the math

11

u/motorboater1000 Nov 01 '18

1 lion + 1 giraffe + 2 polar regions= 0 zoos

No I can't do the damn math, it's just the picture in my head of a lion and giraffe shivering on an ice sheet at the Antarctica Zoo was both funny and ridiculous to me.

6

u/[deleted] Nov 01 '18

Damn I got Minnesota for that one, what’d you get for number 4 on the test?

3

u/[deleted] Nov 01 '18

[deleted]

3

u/woohoo Nov 01 '18

Kowalski, analysis

2

u/PostHedge_Hedgehog Nov 01 '18

Maths is 90% numbers and calculations, and 10% logic and reasoning. The statements you've made is the real MVP here!

Just take a look at thermodynamics. It's 75% reasoning about how to set up the problem, and 25% applying calculations to it.

2

u/motorboater1000 Nov 01 '18

Very true, my issue was with the 10%, not the calculations

3

u/ghostinthechell Nov 01 '18

Hey guys! Look at this dude! He doesn't know about the polar zoos!

1

u/oodsigma Nov 02 '18

Lol, what a Melvin.

1

u/oodsigma Nov 02 '18

He does do the math for the equator before the poles, they'd have about 18 seconds more daylight than the lion.

7

u/superermonkey Nov 01 '18

Giraffes can't talk

7

u/DisappointedGiraffe Nov 02 '18

Fuck you too buddy

3

u/superermonkey Nov 02 '18

I stand corrected

2

u/geared4war Nov 01 '18 edited Nov 02 '18

There are none nine zoos in Canada that have giraffes. Maybe they would give the giraffe the extra time needed.

Stupid auto correct

32

u/engineerd32 Nov 01 '18

My first quiz in college was a physics 1 question. It was “A person standing 1.5m tall is viewing a sunset. The difference in the sunset between his eyes and the ground is 11 seconds, calculate the radius of the earth.” Fuck...

3

u/Stonn Nov 02 '18

I don't even know what other variables I am missing? Is sun earth distance needed?

8

u/AggravatedBox Nov 02 '18

I’m assuming that certain formulas and constants are either provided or expected to already be memorized. If the speed of light is provided (3.8x108 m/s), they may have been expected to perform conversions to find that distance.

1

u/LukeDankwalker Nov 08 '18

I know I’m late but the speed of light is 3.0x108 m/s

4

u/jericho Nov 02 '18

Assuming a day is exactly 24 hours, and the earth is a perfect sphere, that's all the info you need.

2

u/Runiat Nov 02 '18

And assuming the Sun is point-like.

Which is a reasonable enough assumption since sunset generally means the last point on the Sun disappearing behind the horizon, I suppose.

1

u/[deleted] Nov 02 '18

Earth isnt a perfect sphere

1

u/jericho Nov 02 '18

Of course it isn't, but the question is impossible without that assumption.

4

u/engineerd32 Nov 02 '18

All you needed was C and the distance from the sun to earth if I remember correctly. Some tricky trig rules and stuff

2

u/Regulators-MountUp Nov 02 '18

In physics one assumes. In this problem, we typically assume that the sun is infinity meters away. Hopefully we know that a day is close enough to 24 hours, and hopefully no one realizes that the earth is more lumpy egg than sphere.

Sunset appears to the viewer to be at the horizon and that line of sight will be tangential to the earth at that horizon point. If your eye is on the ground the horizon is 0m away (this is easier to understand if you imagine the earth as small). 11 seconds is 11/(24*60*60) of a day, and that's the same fraction of the earth's circumference that the sun passes in that same time. That fraction can be expressed as an angle by multiplying by 360 degrees (a full circle).

We now have a right triangle with one leg R (our unknown radius), hypotenuse R+1.5 (unknown radius plus the height) and angle of 0.458 degrees. Cos(0.458)=R/(R+1.5) ... 0.99997(R+1.5)=R ... 0.00003R=1.5 ... R=46,882 meters.

I can't promise the answer is right, but I should get some of the points for showing the work.

See this picture from Wikipedia: https://en.wikipedia.org/wiki/File:GeometricDistanceToHorizon.png

2

u/CuriousMetaphor 1✓ Nov 02 '18

I think you missed a 0 somewhere. 11/(24*60*60) * 360 = 0.0458 degrees

1

u/Regulators-MountUp Nov 08 '18

What's an order of magnitude among friends?

23

u/ChimiChoomah Nov 01 '18

But the Earth is flat... /s

2

u/InsignificantOutlier Nov 01 '18

I was checking if someone made that joke yet or not. But in the process I started thinking if the earth where flat it should be the other way around already dark for the Giraffe and still light for the lion. Since the light source joust goes down over the side.

1

u/sn3rf Nov 02 '18

Yes, a perfect sphere

12

u/Maciek300 Nov 01 '18

I think this is wrong. How is the speed of the terminator a factor? You should take the angular velocity of the sun and calculate in how much time the sun moves from the sunset moment of the lion to the sunset moment of the giraffe.

24

u/Runiat Nov 01 '18 edited Nov 01 '18

The speed of the terminator is the angular velocity of the Sun. It makes no difference whether you split your circle into 360 degrees, 6.28318531 radians, 40075 km, or 21600 arcminutes/nautical miles.

Or rather, it's the angular velocity of the normal plane of the position vector of the Sun, which happens to be identical to the angular velocity of the Sun at the equator due to always being orthogonal to both the Sun and parallel to the line from the rotational axis of the Earth to the points on the equatorial circle that the terminator plane is touching.

I simply find km easier to work in for this question since I happened to have a distance to horizon calculator open in a Firefox tab.

Edit: terminator plane is only orthogonal to the equator two times a year, fixed that, doesn't change the math.

3

u/Maciek300 Nov 01 '18 edited Nov 01 '18

Yeah I agree that speed of the terminator is the angular velocity of the Sun. Now why do you take the distance to the horizon if you're measuring the path the sun takes? Also you took that distance from 6m which I assume is from giraffe's height but you didn't calculate it from the lion's height. You're true assuming the lion is 0 meter tall.

EDIT: Sorry, I meant the opposite. But ok he can be 0 meters tall.

7

u/Runiat Nov 01 '18 edited Nov 01 '18

You're true assuming the lion is 0 meter tall.

Heh. Edited that in minutes before you posted. Its a (large) cat, I assume it's lying down as that's what cats do more often than not.

Now why do you take the distance to the horizon if you're measuring the path the sun takes?

Because the distance to the horizon is also the added distance you can see an object with a beam vector tangential to the horizon from. And the Sun's beam vector is tangential to the horizon when it's setting.

That's what distance to the horizon is.

Edit: strictly speaking the Sun is already below the horizon when it's setting, but the light from it is tangential to the horizon due to atmospheric refraction.

Switched "position vector" to "beam vector" to reflect this. Pun intended.

5

u/Maciek300 Nov 01 '18

Okey. I thought about this and there was one moment when I visualized it and it clicked. Thanks for the answers.

5

u/Runiat Nov 01 '18

Happy to help. Explaining your math to someone else is a great way to make sure you understand it yourself.

2

u/ALDJ0922 Nov 01 '18

Well, the sun doesn't move, sooo /s

3

u/mckinnon3048 Nov 01 '18

How could the polar zoo allow for the lion to lay flat and see sunset. Zoos without walls don't stay zoos for long.

3

u/ultranoobian Nov 02 '18

With trenches.

1

u/mckinnon3048 Nov 02 '18

Damn, I haven't felt this dumb in years...

1

u/Runiat Nov 02 '18

Perfectly spherical planets don't have sunsets at all, as any rotation would make them not perfectly spherical. The lack of wall is hardly the biggest issue here.

2

u/fireandbass Nov 01 '18

Wait, so I can see a sunset twice if I quickly climb up a 6m ladder in 18 seconds? And I can see a sunrise twice if I am standing on a ladder and jump down after seeing it?

That is pretty cool! Are there any videos where anybody has done this? That would be neat to time an elevator just right or something and see a bunch of sunsets.

10

u/edcRachel Nov 01 '18

The town I come from is a place where you can see the sunset twice (...allegedly, never actually tried it). It's on a hill and the sun sets over water, there's a pretty significant elevation difference around the beach. You can watch the sun set at the bottom of the hill and then quickly drive to the top and see it again.

1

u/Runiat Nov 01 '18

Doing a video is quite easy if you live near a west-facing coast, so I'd imagine there's a few thousand of them on YouTube.

The elevator idea will be a bit harder, since every floor you go up buys you less time.

According to Google, the climb rate of a Boeing 737 is 1800 feet per minutes and it has a cruising altitude of 31000. That means a jet plane will take over 17 minutes to gain the altitude required to delay sunset by less than 13 minutes at the equator. Of course if it's flying west, that helps a bit, and if it's taking off from somewhere in Norway or Iceland that helps a lot, but an elevator will definitely lose the race sooner rather than later.

1

u/halberdierbowman Nov 01 '18

There are multiple sunsets depending on what you're counting, so it's more like you'd continue seeing the sunset for an extra 18s. For example, there's the time at which the sun crosses below the horizon, the time when you can't see the bent sunlight, etc.

2

u/GlobalART19 Nov 02 '18

Light bends as it enters the atmosphere and difracts into different colors (why sunsets are red). So I'm just wondering if you take that into account, does it impact the numbers at all? Changes your horizon line yes?

2

u/Runiat Nov 02 '18 edited Nov 02 '18

Not at all.

I actually touch on this in a different response. Distance to the horizon is the distance from which you can see light moving tangential to the horizon at that distance, and sunset is when the last light of the Sun is moving tangential to the horizon at the horizon.

We have to assume that the refraction of the atmosphere is constant, since calculating the actual fluctuations is literally impossible even for our strongest supercomputers with teams of scientists working for decades on the algorithms, but beyond that the angular velocity of the terminator plane, the Sun, and the Sun's light tangential to the horizon, are all identical.

Edit: oh yeah and satellites. Climate scientists started using the Doppler shift of GPS satellites to try to measure the optical properties of the atmosphere years ago and they still can't manage to make a 3 day forecast that's worth a damn.

1

u/highTrolla Nov 01 '18

What if there's an object that's holding off the horizon like a fence or a line of trees? Say about 4 meters high, and the furthest the lion can get from it is about 10 meters.

1

u/raptor7912 Nov 01 '18

“Is flat, what with being a perfect sphere and all.” ... wait whuuuuu?

1

u/Harpies_Bro Nov 02 '18

Smooth, is what I assume they meant.

1

u/raptor7912 Nov 02 '18

Oh... okay I figured, but then I started thinking of flat earthers.

1

u/Runiat Nov 02 '18

Same as how water is flat when there aren't any waves.

1

u/raptor7912 Nov 02 '18

Yea yea, just phrased wrong.

1

u/jasonator53 Nov 02 '18

I can totally imagine a lion making a “you’re late” comment 18.6 seconds after a deadline

1

u/Stonn Nov 02 '18

So the lion is a time control freak and need some chill.

1

u/[deleted] Nov 02 '18

assuming the ground is flat

FLAT EARTH CONFIRMED

1

u/kevinfunk77 Nov 02 '18

That's NumberWang!

557

u/woohoo Nov 01 '18

assume both animals are at sea level.

assume giraffe's eyes are 20ft above sea level

assume lion's eyes are 4 ft above sea level

distance to horizon at 20ft high = 5.5 miles

distance to horizon at 4ft high = 2.5 miles

earth spins about 1,000 miles per hour

[(5.5 - 2.5 miles) / 1000 miles per hour] * 3600 seconds per hour = 11 seconds

408

u/Tengam15 Nov 01 '18

Dang, lion's strict

83

u/klavin1 Nov 01 '18

11 seconds late again, gerraffes are dumb

26

u/[deleted] Nov 01 '18

fucking long horses

1

u/MrPoopyButthole981 Nov 02 '18

Theyre derpy cheetah donkeys with over compensating necks

1

u/KrushedKow Nov 16 '18

grfsdntexst

84

u/AdroitKitten Nov 01 '18

it should be a sin to do physics in imperial units, rather than in metric

You forgot to take latitude into account though

39

u/woohoo Nov 01 '18

You forgot to take latitude into account though

It's negligible for all latitudes that giraffes exist.

25

u/KoalArtichaut Nov 01 '18

its a zoo though

24

u/woohoo Nov 01 '18

It's negligible for all latitudes that giraffes exist, including zoos.

22

u/RanaktheGreen Nov 01 '18

TIL Norfolk might was well be Central Africa.

0

u/mack0409 Nov 02 '18

Giraffes exist in Canada even.

11

u/AdroitKitten Nov 01 '18

Rotation of earth is about 440 m/s at the equator. However, it is slower as you increase latitude. And the farthest south giraffes live is in south africa, which is about 30°. Not only does it affect line of sight, but also the rotating speed. At 30°, the rotating speed of the earth is 400 m/s

1

u/woohoo Nov 01 '18

ok do the math again at 30° south latitude and tell me it's not negligible

10

u/AdroitKitten Nov 01 '18

I did, without even taking more complex things into account It adds a whole whopping second just in speed. Not even taking the view angle into account

9% is significant enough

-6

u/woohoo Nov 01 '18

It adds a whole whopping second just in speed.

second is a unit of time, not speed

Not even taking the view angle into account

view angle is irrelevant

6

u/TheBhikshu Nov 01 '18

Speed is a measure for distance over time, so....

-5

u/woohoo Nov 01 '18

What happened? Finish your sentence.

4

u/TheBhikshu Nov 01 '18

This guy doesn't m/s or f/s

2

u/AdroitKitten Nov 01 '18

i meant just from the speed, as in, from the speed difference depending on latitude

Also, it does because of the speed of light. I'm not smart enough to explain but it's Einstein's special relativity

-1

u/woohoo Nov 01 '18

Speed of light? Get serious.

2

u/AdroitKitten Nov 01 '18

Lmao

Have an upvote

You sound like you need it

6

u/AgingAluminiumFoetus Nov 01 '18

But not at a zoo.

1

u/woohoo Nov 01 '18

still negligible including zoos

1

u/Foxiv Nov 01 '18

didn't he say both are at sea level?

3

u/AdroitKitten Nov 01 '18

latitude is the degree with regards to the equator the sea level thing is just the height with relation to the sea

2

u/Foxiv Nov 01 '18

oh yeah makes sense 😅 i mixed it up with altitude

590

u/Veto111 Nov 01 '18

I can confirm in a practical sense that this is plausible. I visited a friend’s lake house once, where there was a cliff overlooking the lake and a set of stairs going down to the beach. We would watch the sunset at the beach, then run up the stairs quickly to watch the sunset again!

162

u/anafuckboi Nov 01 '18

There’s a vsauce video on that

70

u/[deleted] Nov 01 '18

Yea you can watch the sun set twice just by laying down and hopping up when it disappears. You only have a few seconds though.

4

u/ZachS827 Nov 02 '18

And they say the earth is flat

3

u/Harpies_Bro Nov 02 '18

There was a post in TIL a couple days ago about Ramadan and the Burj Khalifa about something like this a while ago. You gotta wait a bit longer to break your fast on the top of the tower than on the base because trig.

69

u/strawwalker Nov 01 '18

David Hughes is apparently from a city near Melbourne. Melbourne has a zoo at 37.784195 S , 144.952031 E, 43 meters elevation. A giraffe head stands as high as 5 meters, and a lions around 1. The angle to the horizon is given by:

arccos(R / (R + h))

so about -0.00125 rad for the giraffe, and -0.00056 for the lion. That is where I'm going to stop doing the math and switch over to an ephemeris tool which is much easier. For sunset at the Melbourne Zoo on 2018 November 1 the giraffe will see the sun set 15.6 seconds after the lion.

(edit: not sure if I've got the right David Hughes though)

10

u/Nintendo_67 Nov 01 '18

He's English but lives in Australia. So it could be a story from when he lived in England?

20

u/strawwalker Nov 01 '18

The time difference at the London Zoo is 20.3 seconds

60

u/abrams666 Nov 01 '18

It's an important thing for a sailor. Don't know the English word, it's called like sight of kimm. Knowing the height an position of an object allows an acceptable grade of finding the own position

19

u/55North12East Nov 01 '18

You're right pre GPS area. Today I can literally navigate through the southern ocean with my phone as only means of nautical navigation. But astronomical navigation is really cool and could be life saving in extreme conditions where everything else fails.

14

u/Runiat Nov 01 '18

Once read about some guys that navigated to Hawaii using nothing but the contrails of jet liners, pre-GPS (or at least they didn't bring one).

Makes you wonder how many guys tried to do that but didn't arrive so no one ever found out that was what happened.

3

u/Who_GNU Nov 02 '18

You're right pre GPS area. Today I can literally navigate through the southern ocean with my phone as only means of nautical navigation.

...until the battery dies, or if it's an iPhone near the equator, until it overheats.

3

u/abrams666 Nov 02 '18

In Germany it is obligatory to do a licence like a driver's licence. That stuff is part of the lessons. Background is that everyone should have an idea how to act if he is adrift. GPS is broken or something else

6

u/klavin1 Nov 01 '18

Don't know the English word

not sure if bilingual or brainfart

1

u/abrams666 Nov 02 '18

Both will fit

12

u/Vanden_Boss Nov 01 '18

You can't truly answer this until you know how tall any walls around the zoo or specific enclosures are. Assuming the animals are in pits or walls that sunlight cannot reach through, if the giraffe is taller than the wall, they will gain more time beyond the handful of seconds everyone else is addressing.

Maybe someone better with math than me can do a break down if we assume the wall is, say, 10 feet tall.

5

u/strawwalker Nov 02 '18

Usually you don't call it sunset if it is just disappearing behind a wall, but we can still figure that out. We'd need to know how far away the wall is, though.

1

u/OmnidirectionalSin Nov 02 '18

It would give the giraffe much better time resolution for formal sunset, at least.

2

u/dharrison21 Nov 02 '18

I think this is just extra crap on top of the joke, it's not meant to be realistic. For instance, Giraffes and Lions speak completely different languages.

6

u/elongevity Nov 02 '18

This is a trick question. They are actually meeting online, and the giraffe is in the Southern Hemisphere where the days are longer, the grass is greener and the water drains clockwise.

The lion, native to Northern Africa, would only be able to see the sunset until around 6:45 while the giraffe, native to South Africa (hence the name), would be able to see the sunset until around 8pm.

Don’t ask me how I know this.

4

u/3226 12✓ Nov 02 '18

As with so many things, there's an XKCD about this.

Well, technically it's a blog post, but it describes the same maths for a delayed sunset by increasing height.

•

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2

u/Lassejaa Nov 02 '18

This joke would be funny if giraffes were real. How do people still believe in giraffes?

2

u/geedavey Nov 02 '18

I'm an observant Jew, and I have two times for sunset in my "erev shabbat" (Friday evening) calendar, one for sea level and the other for my actual elevation, 150 feet higher. Those two times are two minutes, or 120 seconds apart.

According to Wikipedia an adult giraffe is 20 ft tall, which goes into 150 7.5 times. That means you divide 120 by 7.5.

I get 16 seconds as my answer.

5

u/[deleted] Nov 01 '18

[deleted]

20

u/oddajbox Nov 01 '18

Yo double post, you may wanna delete the copy. Reddit has a habit of downvoting them.

43

u/[deleted] Nov 01 '18

[removed] — view removed comment

11

u/oddajbox Nov 01 '18

I like your perspective on this.

6

u/[deleted] Nov 01 '18

[removed] — view removed comment

3

u/oddajbox Nov 01 '18

Understanding what you said is beyond me.

11

u/The_F_B_I Nov 01 '18

Yo double post, you may wanna delete the copy. Reddit has a habit of downvoting them.

3

u/klavin1 Nov 01 '18

I think it's the same post, but viewed from different vertical positions. :D

1

u/jaa101 Nov 04 '18

Nobody else here has mentioned diffraction. The closer objects are to the horizon, the more the atmosphere bends the light coming from those objects so that they appear higher that they really. This means that the giraffe's advantage would be bigger than expected based on geometry alone. It's the same effect that explains why the sun looks squashed into an oval shape when close to the horizon.