30 ‘Useless Yet Interesting Calculations’ To Get Your Mind Reeling (New Posts)

"So the ave stump height is cut to 0.45 m. Let's assume an oak, with an ave height of 20m. Thats about 2.3% of overall height.

This tree would therefore be around 11.7km high using that ratio. Almost high enough to tickle the stratosphere at 12km

So if I used the horizon calculator right, you could still see the bastard 387km away

EDIT: Just to answer a few of the many questions. In American that'd be about 7.3miles, or 13,760 washing machines"

"The quote is "I'm sexy and I know it"

sqrt(1+tan^2) can be verbalized as "sec" and so this formula is the "sec of c"

"I'm sec C and I know it""

"They’re called crinkle crankles. A single leaf wall over that distance would need brick piers approx every 1.5-2m if it was a retaining wall it would need to be at least 9” wide (2 bricks). The crinkle crankle has more strength due to it’s curved nature so can be 4” wide or a single leaf of bricks.

For the maths if we can assume they’re true semi-circles then each semi circle would be 1/2piD or 1.57D whereas a double leaf wall would be 2D for the same length D

Therefore using 21.5% less bricks than a double leaf wall"

"Quick eyeballing suggests a curvature of about 30°; that's 1/12th of a full circle, so given that the Earth's circumference is just over 40,000 km, the car would have to be about 3333 km long, or about the driving distance from Chicago to Los Angeles, or about 5.5 million washing machines (in case you're too American to understand kilometers)."

"One source says the “minimum actuation force” of a key is 47.6 grams. If we assume the kitten is standing on 4 keys (only one per paw) 4*47.6 is 190.4 grams or 0.4 pounds. Ao the kitten would be under that weight. It appears that the kitten is standing on more than 4 keys though so maybe 1/2 pound."

"$9.33 on the left and $21.51 on the right"

"Each ingredient can either be included or not -- that's 2 possibilities. Multiply out all 9 ingredients and we have 29 = 512 in total. I presume you'd want to exclude the 1 possibility where none of the ingredients are included, so that leaves 511."

"Quite the opposite, it will leave you with less sandwich. Since no cut is perfect, some of the sandwich molecules will stay on the knife or there is more crumbs on the cutting board. Therefore, cutting on a diagonal (longest cut) will dislodge more material of the sandwich than cutting along shorter line"

"Return flight JFK - Madrid: ~€750 Minimum income in Spain: €850/mo; 24 months amount to €20400. We'll assume that since a lot of people in Spain have to make do with this much, you will figure it out too. Learning Spanish is pretty straightforward, if you live in Spain for 2 years, you're practically guaranteed to pick up enough of it to get by, but let's say you spend €100 on a couple textbooks and a dictionary, just to get you started. Depending on where in the US you live, there might even be a solid chance that you already speak the language, after all it's the country's second language, with more speakers in the US than in Spain. You will also be spending a bit on visas and other bureaucratic requirements, let's call that another €200. Running with the bulls and getting trampled can be had for free. And then there's the hip replacement itself, at $7,371, or €7074. However, depending how you play it, you could actually take a minimum-wage job in Spain, and qualify for public healthcare, in which case the hip replacement might actually be covered. But let's just assume you have to pay for it out of pocket (which, frankly, is a pretty unusual thing in Europe, and typically only happens when people have to get treatement abroad and the insurance situation hasn't been figured out, or for a couple religious weirdos who object against having health insurance on moral grounds).

So let's ring you up; grand total: €28524, that's about $29700.

Not only does it fit comfortably into the US figure, you even have some $12,000 to spare"

"The average emperor penguin slaps with about the same force as a middleweight boxer. 800-1000 PSI"

"Assuming those are $100 bill stacks at $10,000 each. I count 12 stacks across and 15 stacks deep and assuming that each stack is ~0.5 inches tall with a total height of ~30 inches.

12 * 15 * (30 / 0.5) * 10,000 = $108 Million dollars."

"36,567,729 sheets of letter sized paper according to Excel (single sided)

According to Google a pallet contains 200,000 sheets

Therefore 182 pallets of paper would be needed.

A photocopier can apparently print 500,000 sheets in its lifetime, so you would need 73 photocopiers"

"The total area of ocean is about 361 million square km, or 3.61 x 1014 square meters.

The highest point of Denmark is about 171m.

The earth is large enough that we can choose to ignore the curvature over a change of radius of 171m (compared to the radius of 6300km it’s less than a rounding error).

What we can’t ignore is that there is about 30 million square km of land that is 171m or less above sea level which will also be flooded (estimating from a hypsographic curve). I’ll factor in a mean of half of that to give the new earths surface figure of 3.76 x 1014 square meters.

This means that there would need to be 171 x 3.76 x 1014 = 6.43 x 1016 cubic meters of water displaced.

If we assume a good throwing rock has a volume of 1 litre, then you would need 6.43 x 1019 rocks.

At 1 rock per day that’s going to be 1.76 x 1017 years, or 12 900 000 times the age of the universe.

If all 8 billion people on the world threw one rock per second, it would only take 250 years"

"According to a google search, it takes about 4,000 newtons to crush a bone, & I’m going to assume that an average person has a frontal surface area of 1 m2 for ease.

A nickel weighs 5 grams, which equates to about 0.05 newtons of gravitational force… you’d need at least 81,578 nickels on top of the person, or about $4,078.90"

"Beginner: 1 in 102 million
Intermediate: 1 in 6.1 million
Expert: 1 in 477,000"

"Oh come on this is doable from an engineering point of view:

One sip per second of 10ml (a shot glas' equivalent in a few seconds)

90°C tea, 0°C water (I see ice?), ∆T =90

Conduction in the thin straw is negligible, basically water-to-water heat transfer at a slow rate: the convection coëfficiënt for that is about 1000W/m²K (forced convection water to unforced water essentially)

Straw is 5mm diameter, 150mm length is submerged. Total area = 5π*150 = 2350mm² heat exchange area.

As such, the heat (power) transferred per second is = 9010002350/1e6 ≈ 211W

211W for 0.01kg water (tea) per second is ∆T = 211/4200/0.01 ≠ 5°C difference.

This matches my experience: the straw is simply not big enough to offer proper area for heat exchange:

Source: 10 years of steam boiler engineering

Hope you enjoyed!"

"Im gonna assume the loop is about 60m based on the height of the building next to it.

At the top of the circle, the two forces are mg and centripetal force. The two together equal ma (a being v2/r.) So mg + Fc = m(v2/r). Set Fc to 0 as you would have to have a centripetal force slightly above 0 to complete the loop. This gives us v2 = sqrt(gr). For a 60m loop (30m radius) v = 17.1m/s.

This is the speed at the TOP of the loop. Using conservation of energy, we can say that 1/2mv2 + mgh = 1/2mv2 (the first part is top of loop, second part is bottom of loop). Cancel m and plug in numbers.

You would have to travel 38.34m/s or 138kph (85.7mph) to make the loop."

"NASA did the math on this

"If the Sun was replaced with a black hole that had the same mass as the Sun, the Schwarzschild radius would be 3 km (compared to the Sun's radius of nearly 700,000 km). Hence the Earth would have to get very close to get sucked into a black hole at the center of our Solar System.""

"He's a corporate executive of some sort and the trip was being paid for by the family member in Paris. His wife was also a fairly successful artist.

A 800k house in Bay Area probably cost >5M today"

"A circle has 360 degrees, so 60/360 is 1/6th of a pizza, and 45/360 is 1/8.

The area of a circle is (pi)r2

The area of the 6" pizza is 1/6(pi)(62 )=6(pi)

The area of the 7" pizza is 1/8(pi)(72 )=6.125(pi)

6.125/6=1.021, so the 7" pizza is 2.1% bigger

$1.70/$1.50 is 1.13, or 13% more expensive.

The 7" pizza is 13% more expensive, but only 2.1% bigger, so the 6" pizza is a better deal."

"500,000 tons is its downward force due to gravity. It has a gravitational pull, but minimal compared to the earth (6,000,000,000,000,000,000,000 tons)"

"If only contacting the floor with the heel then yes.

An elephant's foot is 15-19 inches across, so assuming it's vaguely circular gives an area of at least 0.114m2 per foot. Elephants when walking depending on the gait will have 2/3 feet in contact with the floor - so that's at least 0.228m2 in contact with the floor. (Going for minimum area as this will give the highest pressure for the comparison)

6000lbs under Earth's gravity is a force of 26.7kN, which when divided by area for a pressure of ~117kPa - if it's just standing still this could actually be halved to approx 58kPa

If a 100lb woman (445N) is standing on only her heels (~1cm2 x 2) this is a pressure of 2,224kPa which is indeed about 20 times higher than the elephant on 2 feet.

However that's not really representative of how heels are worn, even the picture shown has the shoes in contact with at least 20x the area of the ground than just the heels"

"Yes, a 33 round single elimination bracket would have 233 participants, which is about 8.5 billion. So it is actually possible, since the world pop is probably just under 8 billion, that the winner would be someone who had the 1st round bye and only had to win 32 times"

"I believe blackjack gives the house a 0.61% edge over the player on average when played absolutely perfectly. Assuming the same odds for every game, .493932 leads me to a .000000000157% chance of winning 32 games in a row."

"Rough estimate: 8 *109 people , Assuming a 10 cm2 signature/person to make the numbers easy. This comes from a 10cm long signature 1 cm in width.

Gives 8*1010 cm2 = 8*106 m2 in area. If we model the bat as a cylinder of length L, the surface area is SA = 2 pi r2 + 2 pi r *L, so if the bat has a length of 1 meter to fit in our hand, the second term is negligible, as r will be huge.

So A / 2pi = A/6 ~ 1 *106 m2 , square root to get the radius,

R = 1 * 103 m = 1 km

So if the bat is a meter long, it would have to be around a kilometer in radius to fit everyone’s signatures."

"Each pod is capable of holding 25 people at maximum safe capacity. Assuming each person can reasonably be 100kg, that means the safe load placed on any one pod is 2500kg.

The pods themselves weigh 10,000kg. The radius of the London eye is 67.5m.

Since at the bottom apex of the rotation the total force from centrifugal/centripetal force is equivalent to weight, a centrifugal force equal to 2500x9.81=24,525N is the maximum safe level.

F=MV2/R

V=sqrt(FR/M)

V=sqrt(24525x67.5/10,000)

V=12.9m/s

The pods could travel at approximately 28mph, or complete one rotation every 33 seconds, before the forces on the pods exceed safe levels. Theoretical maximum levels would be higher, but without stress testing the material cannot be precisely calculated."

"Counter tops are usually 34 to 36in.

It was 5 phones to the top of counter 5.75"*5=28.75"

So I think they are off by a factor of 1.18 (34/28.75)

That would put her height around 5ft1in."

"Slow apartment sized elevators (which this looks like) go about 1mph. Let's say it takes an average of 10 months for a dog to go from puppy to a fully grown adult.

10 months = 305 days = 7320 hours.

Short elevator ride = 7320miles (close to the diameter of the earth)

Assuming dog is 16 years old in second photo:

16 years = 192 months = 5856 days = 140,544hours."

"Definitely. Let's assume that you go to Walmart and get yourself a 70.8 gram bottle of extra fine doom. You then load up your hypervelocity shotgun with it and accelerate those grains to 99% of the speed of light.

By the lorentz factor, your glitter now contains 91 grams c2 of kinetic energy. By E=mc2 , you now have 8 terajoules of energy, or around 115 times the energy released during the Hiroshima explosion. If this glitter were an asteroid traveling at classical speeds, it would have the destructive potential of the asteroid that created Meteor Crater in Arizona. There are very few things that could withstand that. While the exact mechanics of what would happen depends heavily on the target, it's safe to say that all but the most hardened structures would not survive."

"It takes 42 adult-minutes to build a snowman.

It takes 63 child-minutes to build a snowman. Therefore, 1.5 child-minutes = 1 adult-minute.

If all 6 people are working together, they collectively do 3 adult-minutes and 3 child-minutes of work per minute, or (converting) 5 adult-minutes per minute.

Hence, it will take 42/5 = 8 minutes, 24 seconds to build the snowman."

"There is a mathematical operation called concatenation (with symbol ||) that just combines two numbers. For example, 23 || 71 = 2371.

Therefore, 9 || 9 + 9 / 9 = 99 + 1 = 100"

"Shakespeare wrote 884,647 words, according to this article. The average word in the English language has 4.7 characters, plus spaces, so we'll assume he wrote 5042487 characters.

The average human types about 40 WPM = 200 CPM = 105,120,000 characters per year, which is about 100 times our Shakespeare set. I'll assume this is the amount a monkey can do.

Also assuming the monkey can only press one key at a time, and using lowercase letters, ,.-!?"() and space, there are 35 relevant keys on our idealised keyboard.

The probability for every set of 5,042,487 characters to be Shakespeare's works would be 1/35^(5042487). For comparison, there are about 10^80 atoms in the observable universe.

It would take about 35^(5042487) strokes, and this will not be significantly change whether we use 40WPM or 1 character per year, so we can say it will take more than 35^(5042487) years"

"Basically it would be impossible. You would need enough fans to cover the radius of the hurricane, all spinning fast enough to blow winds of an equal strength of that hurricane, which a regular standing fan does not have the power to do"

"So, lets do this rigourously. First off, I'm using the average weight for European people (average of all, male and female). The toxicity data on humans is always a bit complicated for ethical reasons, therefore I can't use a LD50. Instead, I use the LDlo, the lowest dose of caffeine which ever caused death of an human. It is averaged over man and woman LDlo as both diverge quite significantly. Also, I'm on mobile, so please excuse the formatting.

m(average human, Europe) = 70.8 kg

LDlo(human) = 192 mg/kg

m(deadly dose) = 70.8 kg • 192 mg/kg ≈ 1.36 • 104 mg = 13.6 g

m(Caffeine in 237 mL Coffee) = 96 mg

m(deadly dose of coffee cups) = 1.36 • 104 mg / 96 mg ≈ 142 [cups]

Henceforth, this comment is wrong. Even if you make extraordinary strong coffee with 200 to 250 mg caffeine, the deadly dose would still be higher than 42 cups."

"Assuming you’re given all the side lengths/angles you need, split up each face into a bunch of triangles/trapeziums and find the area of all of them and add them all up"

"It says in an article he "accumulated 30 million miles". Whilst it's not clear if all of that was under the lifetime pass, you could presume that's what it means. If you know the AA air miles accumulation rate, you could possibly work out how many miles he flew, rather than the number of flights."

"1 tablsespoon of mayo is about 13.8g

this means with 308k likes is makes about 4250.4 kilos of mayo that he has to eat

the energy of those 308k ablespoons is about 120.7 gj or 120'736'000kj devided by the recomended energy intake of 8700kj a day the mayo alone wozld last you 13877 days which is 38 years."

"Ok I see now. 1$ wasn't the og price. Feels like a flip to make you assume.

x is the original price

1 is an additional dollar on top of half the original price.

Therefore x = 0.5x + 1

adding the implied 1.0 to the X for clarity and format

Subtracting the half from both sides

1.0x = 0.5x + 1

-0.5x -0.5x

turns out to be

0.5x = 1

0.5x = 1.0

÷0.5 ÷0.5

1/1 ÷ 1/2 < side work for the right side 1/1 × 2/1 because two fractions divide is equal to the latter fraction flipping and multiplying 1 x 2 = 2

therefore x = 2

God damn I thought it was 1.5$ because I assumed 1 was the initial cost when really cost = (1 + 0.5price)"

"That looks to be a 16 oz (473 mL) wide mouth mason jar. Reese’s Pieces are about the same size as m&m’s (for which there is more data available). M&m’s range from 0.6-0.65 mL in volume, and have a packing density of about 68%.

pieces = jar volume * packing density / piece volume

So

473 mL * 0.68 / 0.6 mL = 536 pieces maximum

473 mL * 0.68 / 0.625 mL = 515 pieces average

473 mL * 0.68 / 0.65 mL = 495 pieces minimum"

"For a start, Wiles' proof of Fermat's Last Theorem was 129 pages long.

Wikipedia's summary of the proof is itself approximately 5,700 characters long.

So you wouldn't be able to fit that into a password which was just 732 to 942 characters long."

"This demonstrates the gamblers fallacy. It is the incorrect belief that, if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future"

"A 14" pepperoni pizza from Dominos is 2240 calories, per their online calculator. 28" is 4x the area, so 8960. Divided by 2, that's 4480. 32 oz of full-sugar Coke is about 400 calories. So if you factor in inaccuracies with all the multiplication, you'd probably want to round it to 5000 per person"

"It is supposed to say “One* digit is repeated” not “Ones”.

The correct answer is 24,849."

"I am a locksmith.

Each button can only be pressed once. Pressing multiple buttons simultaneously is allowed. Not all buttons must be pressed.

There are over 1000 combinations, so you would think that it would take less than an hour to try them all if each attempt took 3 seconds."

"No. The Carbon Majors Report which this statistic comes from only looks at industrial emissions, not total emissions, excluding things like emissions from agriculture and deforestation. It's also assigning any emissions from downstream consumption of fossil fuels to the producer, which is like saying that the emissions from me filling up my car at a BP filling station are entirely BP's fault. These "scope 3" emissions from end consumption account for 90% of the fossil fuel emissions.

In addition, it's technically looking at producers, not corporations, so all coal produced in China counts as a single producer, while this will be mined by multiple companies."

"Dumping a big ice cube in the ocean will only postpone the inevitable, what you want to do is vent all the gas from the combustion engines directly upwards at noon, all at the same time from the same location, that will cause the Earth's orbit to be a little bit further away from the sun, that'll cool down the water. It would also make the orbit bigger, which would add an extra week to the year, I propose we call it Robot Party Week"

"Using Kwaloon Walled City as a reference (which is apt given the image), you can have a stacked population density of 1.5 people per square meter. Due to the height here, I think we can triple that to 4.5 people per square meter.

That ship is vast. I can only estimate the dimensions poorly, but let’s go 150m by 1000m.

That’s 150 x 1000 x 4.5 people, or 675 000 people.

For reference, Peach Trees (from the amazing Dredd) had only 75 000 residents."

"Just say by Peano's axioms. The later of which basically state that there is a successor function S(n)=n+1. So if you plug 1 in S(1)=1+1=2. It's just that simple. You can alternatively use the different set of axioms in 1910 Whitehead/Russell Principia Mathematica, rather grandiosly named for the book by Newton. That makes the problem harder, but some axioms needed for it can be proved using Peano's axioms, so there is really no point to doing things the hard way."

"The boat is approximately 19 pixels high to the deck and 64 long if I match it with a circle with r 1118 pixels that matches that curve. (I did this quickly in Paint, so it's a very rough estimate.)

The earth has a radius of 6371km = 1118p

Thus 5.69km = 1p

Boat length = 64p * 5.69 = 364.708km long

Boat Height = 19p * 5.69 = 108.272km high

So according to my rough calculations, the boat's deck would officially be in space.

The front sail is 42p high, so 239km"

"The age of the Earth is probably closer to 4.5 billion, but that's whatever.
Homo Sapiens has been around for around 300,000 years. Relative to the age of the Earth, that's 3 * 105 / (4.5 * 109) = 3/4.5 * 104 = 1/15,000 = 0.000666...

Taking 45 years and multiplying it by that factor gives us the scaled-down value. But let's first convert 45 years into seconds (screw leap years):
45 years = 45 y * 365 d/y * 24 h/d * 60 min/h * 60 s/min = 1,419,120,000 seconds
1,419,120,000 s * 1/15,000 = 94,608 s = 94,608 / 3,600 s/h = 26.28 h.
So that's already off.
Maybe they meant something else by "we have been here" - but I'd say the emergence of Homo Sapiens is the most reasonable interpretation.

Moving on, the industrial revolution began around 1760, that's 2023-1760 = 263 years ago.
Same method as before. First get the fraction of Earth's lifespan:
263 / (4.5 * 109) = 5.8444... * 10-8 =~ 1/17,110,266
Then use that as a factor on our 45 years in seconds:
1,419,120,000 s * 1/17,110,266 =~ 82.94 seconds.
A bit more than a minute, but close enough, I'd say.

Regarding the "50% of the world's forests", Wikipedia has the following to say:

About 31% of Earth's land surface is covered by forests at present. This is one-third less than the forest cover before the expansion of agriculture, with half of that loss occurring in the last century.

One-third less since the expansion of agriculture is not the same as 50% since the industrial revolution.
But then we could argue about the meaning of "destroyed"..."

"Theoretically yes, depending on what the data is like.

If I have a binary data file that's just 10^100 ones I can fully represent it with the words "ten raised to the power of one hundred ones". That's technically data compression in so far as a program could take it and use it to recreate the original file somewhere else. It's just not very useful because there was no actual information in a file that's all ones.

To get 55.4 yottabytes compressed down to 2.62 MB you'd need the data in the original file to contain almost no actual information or you'd need to use a compression so lossy that you'd lose almost all the information in the original file."

"There is an infinite number of answers, but in first grade I probably would’ve drawn two dots positioned arbitrarily in the fourth box."

"First of all the the longest Odachi is Haja-no-Ontachi, with a length of 465cm

Second of all the longest odachi (that I know of) used in combat was Taro tachi, a 288 cm long odachi wielded by Magara Naotaka who was 210 cm himself. So he would have to be 274.9 cm tall to wield a 377 cm odachi while having the hight to sword length ratio.

That would be 9 feat tall btw"