How did Archimedes calculate the volume of spheres using infinitesimals? | AskScience Blog

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Friday, February 10, 2017

How did Archimedes calculate the volume of spheres using infinitesimals?

How did Archimedes calculate the volume of spheres using infinitesimals?


How did Archimedes calculate the volume of spheres using infinitesimals?

Posted: 09 Feb 2017 09:25 AM PST

What is the smallest amount of matter needed to create a black hole ? Could a poppy seed become a black hole if crushed to small enough space ?

Posted: 10 Feb 2017 05:40 AM PST

What is limiting people from making room temperature superconductors?

Posted: 09 Feb 2017 08:07 PM PST

According to my physics teacher if someone was to come up with such a thing then overheating anything wouldn't be a problem and that person/group would become trillionaires overnight.

submitted by /u/gamblingthroaway
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How did scientists in ancient India (~1500 BCE), precisely predict trajectory of the Moon and other celestial events without the use of technology like telescopes, computers and satellites?

Posted: 09 Feb 2017 10:55 PM PST

They even created a precise calendar, based on these predictions, which holds true till today, several thousands of years later. I am very intrigued as to how was it possible at that point in time.

submitted by /u/imkaush
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How would Helium-3 be mined on the moon or the outer gas giants Jupiter, Saturn?

Posted: 09 Feb 2017 07:44 PM PST

It comes up in fiction, but what exactly would the process of mining Helium 3 look like?

submitted by /u/AndyLC
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For the vast majority of Earth's history, there was no life on the surface. What did the landscape of the Earth look like before plant life, or land animals?

Posted: 09 Feb 2017 03:12 PM PST

This is a strange question, but it's bothering me. I don't think I've ever seen an artists impression/depiction of what Earth's surface has looked like for most of its lifetime. I remember in Walking with Monsters they depicted it as a dry, desert, arid landscape.

What would it have looked like? If the Earth was stripped bare, would the rocks be grey? Yellow? Brown? Would it be dusty, muddy, or sandy?

submitted by /u/Pluto_and_Charon
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Why do bases "eat" flesh?

Posted: 09 Feb 2017 10:30 AM PST

with acids it is because the released H-atoms react with the proteins and breaks up the pepitde bond. but how do bases work?

submitted by /u/theluke112
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Is it easier for an exhaust fan to pull air through a duct rather than pushing it into the duct?

Posted: 09 Feb 2017 06:52 PM PST

I'm planning on adding a new bathroom exhaust fan and somehow I'm thinking that it if it were mounted closer to the roof (in the attic) it would be able to pull the humid air out of the bathroom through the duct more efficiently. As opposed to being ceiling mounted, it would have a harder time pushing air through the duct. Is there any basis for this?

submitted by /u/qazpod
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How would one objectively determine if the sample size of a set of data is "good enough"?

Posted: 09 Feb 2017 05:17 PM PST

What does the Schrodinger equation mean and what does it tell us?

Posted: 09 Feb 2017 01:10 PM PST

I am beginning quantum mechanics and we have been studying the Schrodinger equation pretty extensively. But I am confused about what this equation represents and why can't we derive it?

submitted by /u/tokamak_2000
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If blood is taken from a human corpse several hours after death, can lab tests detect that the blood sample was taken from a dead person?

Posted: 09 Feb 2017 10:41 AM PST

I'm aware that blood coagulates several hours after death. So does a blood sample taken from a person who has been dead for several hours contain markers that distinguish it from blood taken from a live person (or very recently dead person), and can these markers be detected through forensic testing?

submitted by /u/PetrichorGirl
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An event happens with constant frequency F. I am uncertain about the exact value of F, as represented by the probability distribution P(F). I start observing at a random moment. After S seconds, the event occurs. What is my new subjective distribution of P(F)?

Posted: 09 Feb 2017 10:57 AM PST

Which is stronger, covalent or ionic bonds?

Posted: 09 Feb 2017 09:42 PM PST

What determines the difference of energy between two quantum energy levels?

Posted: 09 Feb 2017 04:33 PM PST

I want to find out what makes different items have different colors. I already found out that they only absorb light that can help the electron "jump" to another quantum energy level but what determines the difference between the quantum energy levels?

submitted by /u/ThimoSpeelman
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What does it mean that the phase velocity or the group velocity of matter waves can be greater than the speed of light?

Posted: 09 Feb 2017 01:54 PM PST

In my textbook today I read that in matter waves that the phase velocity and group velocity can exceed the speed of light but we wouldn't be able to attain any information if it did. So in order to transmit information the wave must be modulated in some way. What does this mean? Matter waves can travel faster than light but don't have any information? I though nothing can exceed the speed of light?

submitted by /u/tokamak_2000
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Can natural subterranean aquifers be artificially refilled?

Posted: 09 Feb 2017 05:38 PM PST

If we had a supply of fresh water, could we pump that water back into the aquifer at the rate we took it out? Would the ground that has sunk because the water level lowered rise back up?

submitted by /u/1SweetChuck
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Confused by this video by Leonard Susskind on all symmetries in physics being approximations. How can this be right?

Posted: 09 Feb 2017 04:01 PM PST

https://youtu.be/45vCHttuUnQ

Susskind says that all symmetries (continuous symmetries and symmetries that are about interchanging two objects) are really always approximate or are always broken.

He gives this example about nearly massless quarks which I understand just fine.

But isn't CPT symmetry exact as far as we know? And what about space translational and rotational symmetry which give rise to conservation of linear and angular momentum?

submitted by /u/ultraking_x2
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If we're inside the Milky Way, why does it look like it's "over there"?

Posted: 09 Feb 2017 09:19 AM PST

Here is how the Milky Way typically looks from our solar system: https://i.imgur.com/PgYKaSd.jpg

If we're on the outer edge of the milky way, why does it feel like the photographer is sitting way outside the galaxy in space, and looking upon it from afar? I picture myself on a giant dinner plate, just in from the rim a few hundred meters. I look off to the center, and then look down along the floor and see plate all the way up to my feet. I turn around, and see plate extending off to the rim. It looks like all the area around me is plate, but the view we have of the galaxy looks like we're perched far away in deep space.

Why doesn't it appear as though some big spiral arm is extending towards us and enveloping us? Like this: https://i.imgur.com/tFMp00H.png

submitted by /u/Freeloading_Sponger
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Why does there appear to be water erosion at the edge of continental plates under the ocean?

Posted: 09 Feb 2017 09:48 PM PST

The most notable area that I see on google maps is the west coast of north america where it looks like rivers flow across the pacific plate. I know freshwater is less dense than saltwater, so why would this happen?

submitted by /u/YumeCookie
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Is there a Gauss's Law for Light?

Posted: 09 Feb 2017 12:44 PM PST

If we state Gauss's Law as

Surface integral of E dot dA = Q / (epsilon_0) 

Can we say this?

Surface integral of Illuminance dA = Luminous Flux 

Does that equation hold true? I figured the dot product could go because illuminance is a scalar. Is there some other expression that it equals, such as Q/(epsilon_0) for Gauss's Law or 0 for his law for magnetism or mass for -4piGM for Gauss's Law for Gravity?

tl;dr: I'm trying to mentally relate the concepts of luminous flux and illuminance to electric flux and electric field.

submitted by /u/66bananasandagrape
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Can some Taylor series be interpreted as Legendre-Fourier series?

Posted: 09 Feb 2017 12:34 PM PST

Suppose you have a function that can be expressed as a Taylor series as well as a Legendre-Fourier series. Since the Legendre series is just a series of Legendre polynomials, we can group coefficients and rewrite it as a power series. And since this "new" series must be equal to the Taylor series (at least for |x| < 1), the coefficients must be equal.

Taylor series are said to NOT be series of orthogonal functions, but in this case, it seems that it is equivalent to one.

So can Taylor series be interpreted as Fourier series in this way? Or am I being loose with a definition or something?

submitted by /u/bellsandwhistles
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Does the angle of the tube affect Poiseuille's Law?

Posted: 09 Feb 2017 09:26 AM PST

Hi,

Just wanted to check that Poiseuille's Law concerning flow of fluids through tubes isn't affected by the angle of the tube. All the diagrams that I've seen show horizontal tubes, and I would like to know if the law works the same if the tube is vertical, below the water source.

Thanks for any help :)

submitted by /u/Millman97
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