## October 2013

### 1 post

## December 2012

### 1 post

Hi! Love your blog. I enjoy math, but the unfortunate thing is that Im really bad at it. Is this strange to be bad at a subject you enjoy? And what do you recommend someone does if they want to get better at math?

No that’s not strange at all! Part of the fun of learning something new is its difficulty. If you want to learn more about math all you have to do is stay curious. Wikipedia is always a great resource. Talk to your math teachers or professors and see what fields would be most useful at your age and see if you can buy some text books relating to the subject. Youtube has useful channels too, like Khan Academy.

## October 2012

### 1 post

What are the 9 types of energy

Hey there,

Why don’t you check out this earlier post. It should give you a brief intro to the types of energy, the law of conservation of energy, efficiency and Sankey diagrams!

Hopefully that will help you out and thank you for the question!

As always, feel free to submit any other inquiries to our ask.

## August 2012

### 1 post

Hi! I stumbled upon your tumblr, and I'd like to start off by saying how amazing it is, and thank you for making this tumblr! Moreon to my issue, i'm currently studying crude oil in Chemistry. Could you please help me understand"cracking" in terms of crude oil? From what I understand, 'cracking' is the CHEMICAL process of breaking down large molecules into smaller ones. And they 'crack' crude oil to refine it into petroleum; fractional distillation being a PHYSICAL process. More info please?

It sounds like you’re a bit confused between fractional distillation and cracking. It’s true that cracking is a chemical process and fractional distillation is a physical process, but by saying that I mean to show you that they’re two entirely different processes.

When crude oil is first extracted from the ground, is made up of a variety of different hydrocarbons (chemical compounds that only consist of carbon and hydrogen), some very short (ethene) and some long (decane), and is entirely useless in this state. Hydrocarbons can be separated into two groups: alkanes and alkenes. An alkane is saturated, meaning it holds as many hydrogen atoms as possible, whereas an alkene is unsaturated and contains a double carbon bond.

Fractional distillation serves to separate the longer hydrocarbons from the shorter hydrocarbons by their boiling points. This works because the longer the hydrocarbon, the higher the boiling point and viscosity and the lower the flammability.

Fractional distillation takes place as follows:

- Crude oil is vapourised and fed into the bottom of the fractionating column.
- As the vapour rises up the column, the temperature falls.
- Fractions with different boiling points condense at different levels of the column and can be collected.
- The fractions with high boiling points (long chain hydrocarbons) condense and are collected at the bottom of the column
- Fractions with low boiling points (short chain hydrocarbons) rise to the top of the column where they condense and are collected.

To see a diagram of the fractional distillation process, click here.

Cracking on the other hand, breaks long alkanes down into shorter, more useful alkane and alkene molecules. It requires a catalyst (a substance that causes or accelerates a chemical reaction without itself being affected) and a high temperature. This is done mainly to assuage the high industrial demand for the shorter molecules. The alkenes are typically converted into polymers (plastics) while the alkanes are sought after as a fuel source. Cracking is an example of a thermal decomposition reaction.

I hope that helps clear up some of your confusion.

## July 2012

### 2 posts

## June 2012

### 2 posts

## March 2012

### 1 post

Happy π Day math lovers!

We here at Say It With Science would like to celebrate it with you by sharing some interesting trivia about one of our favorite physicists, Richard Feynman, and one of our favorite constants, π (pi). The Feynman Point is a sequence of six 9’s beginning at the 762nd decimal place of π, named after Nobel Prize winning physicist Richard Feynman. Feynman had memorized π to this point so that he could end his recitation of the mathematical constant by saying “nine nine nine nine nine nine and so on…”. At this point someone less knowledgeable about mathematics might assume the number continues this way forever, however we know better. It is believed that π is a normal number, meaning that its digits are as uniformly distributed among the digits 1 through 9 (or the digits of any other base you choose to use). If π is a normal number then the chances of coming across six 9’s in a row is 0.08%. Strange occurrences like this are what makes math beautiful. π Day is a perfect reason to start memorizing as many digits of π as you can! Happy π Day!

## January 2012

### 1 post

## December 2011

### 2 posts

## November 2011

### 1 post

## October 2011

### 6 posts

How can I be a writer on sayitwithscience?

Hey, there!

At this moment, we’re not sure if we can immediately recruit someone new to the team. There are a few things, however, that you can do to show us your interest:

- Email us! Message us (non anonymously)! Let us know who you are! Tell us about your science interests!
- Write posts you would like to submit. You may then submit them to us via the submission box! If you let us know beforehand, we can guide you through the process. Remember: they must be original work and must include links to any sources you use.
- Provide general feedback and comments.

If things end up going great, you may land yourself a position on the team! Thank you for your interest! This message put a smile on our faces. (:

-Say It With Science

∑ F = ma

… is a differential equation:

where acceleration **a**(t), velocity **v**(t), and displacement **s**(t) are all vectors and functions of time. This equation is second-order in position because the highest derivative is the second time derivative of position. Combined with the right boundary conditions, **s**(t) (also called the trajectory: path through space and time) can be determined.

This differential equation can be solved one component, or dimension, at a time. Let us focus on one of these, and call it the x component. The equations for y and z can be found exactly the same way.

**Constant acceleration**

If the graph of a(t) signifying acceleration in the x direction is constant

then the graph of v(t), the velocity in the x direction, is a straight line with slope a_{0}

and the graph of x(t), the position along the x axis, is a parabola

It is also possible for the acceleration, or either of the initial velocity or initial position, to be negative. Thus the displacement/projectile motion formula is derived.

Hello followers!

The contributors have been on a bit of a break, but we’ll be back soon with a new batch of posts. In the meantime, we’d like to get to know our readers!

What subject areas do you study/where are you in your education/what classes are you taking?

Any requests for future Say it with Science posts?

## September 2011

### 8 posts

Hey sayitwithscience - if I'm not mistaken, the featured post regarding the Higgs boson is a bit misleading; I would think it's too early to draw such a conclusion since the LHC isn't running at full power yet? Here's a bit of info from a quick google search: "...LHC will be shut down at end of 2011 with a view to run at full capacity in 2013" Hope you can clear this up for me ~ thanks!

We can’t seem to find the post you are referring to on the featured section! Sorry!

Perhaps it had something to do with this?

Since the particles accelerators collect a **tremendous** amounts of events (images of the collisions taken by the detectors), physicists have not yet finished analyzing the data completely to be able to conclude anything about the existence of the Higgs. Rolf Heuer (director general of CERN) himself has told journalists that this conclusion will be drawn by the end of 2011. Even by then, the LHC will *still* not be running at its maximum power. The reason behind this is because according to theory, the Higgs is supposed to be able to be detected at a certain mass range (114GeV-145GeV) and both the Tevatron and LHC have already reached these energies!

The current plan for the LHC is that from now until about end of October they will continue the proton-proton collisions and from November to December they will collide heavy ions for the ALICE detector. As you have read, at the end of 2011 there will be an “extended technical stop” but after that, the LHC will continue running again until the end of 2012. After that, there will be a prolonged shutdown (roughly 17-19 months) where they will upgrade the Quench Protection System further prepare the LHC to run at even *higher* energies and luminosity.

The best source of information regarding the LHC is on the Quantum Diaries blog. If anyone has doubts or questions regarding the rumours circulating about the LHC, I recommend that they should consult this site.

Thank you to the contributors! This blog is AMAZING.

Our pleasure! We’re doing what we love! We did not have any expectations on the kind of response and feedback we would get from the tumblr community; it turns out that it is great!

We know we have not gotten a post in for a while. We are still there, though! It’s just that, as you know, we’re all students and school just started. Once we get into routine, you can be on the look out for more posts.

Thanks for sticking with us.

-sayitwithscience

Can someone please explain what I am studying when I am studying limits, delta & epsilon. I am having a really difficult time visualizing what is going on and what these things represent... Not so much with limits. I "know" what a limit is,,, but how they all tie in together & the other two specifically. If someone could help I would be ETERNALLY grateful!

Often, the first visual interpretation of a limit is one in which you picture moving along a function by changing your *x* value, and for a function that seems to have no holes, the simplest way to find the value of a limit is to substitute the target value for *x* and see what the output value of the function is. However, this is not a rigorous interpretation because, often, there is an obstacle (like an undefined solution) with the output value. The ε-δ definition allows us to define regions about the point you’re evaluating, and it ultimately allows us to have rigorous definitions for when a limit does and does not exist.

The δ in the definition applies to a region about the *x* value in question (say, *a*) — the region is defined by *a *- δ ≤ *a* ≤ *a* + δ. The ε in the definition applies to a region about the function’s output value, say, *L*: *L - *ε ≤ *L* ≤ *L *+ε.

The definition itself corresponds to what may be interpreted as a sort of game. If you have two players — the “devil’s advocate” on one side, on the y-axis, and you on the x-axis — then it’s the devil’s advocate who claims that you can’t bring the true value of the limit to be in the region of *L - *ε ≤ *L* ≤ *L *+ ε. In response, you adjust your value of δ to allow the limit to exist in that region, and on his turn, he shrinks the region even further, by decreasing the value of ε. If the limit is to exist, then as long as ε and δ remain greater than 0, you will always be able to achieve a limit value within the given ranges (ε and δ need to be kept greater than 0 because the goal is to define the limit based on the immediate region about the function, not evaluate at *a* itself — such would be simply substituting *a* into *f(x)*). Hence come the familiar relations that govern the ε-δ definition: Given that

then for any real number ε > 0, there exists another real number δ > 0 such that if

then

## August 2011

### 20 posts

The Doppler Shift formulae for sound waves are pretty easy to visualize and derive, but why can't the same principles be used for electromagnetic waves? What are the resulting formulae?

Yes, there are many good pictures and animations of the Doppler effect for physical waves!

You know the Doppler shift formulae are based on the relative velocities of a wave source and observer. Where sound and other mechanical waves are concerned, the velocity of the medium must also be taken into account, and the velocities of the source and observer are relative to the medium. Electromagnetic waves do not need a medium, so the shift formulae only require information about the relative velocity between the source and observer, but they need to be in terms of the speed of light, c.

Actually the “classical” Doppler effect model for sound waves is approximately valid for electromagnetic waves when the speeds of the source and observer are much smaller than c. The ratio of the observed or received frequency f_{o} to the source or emitted frequency f_{s} is

f_{o}/f_{s} = 1 - v_{rel}/v_{wave} = 1 - v/c (≅ 1)

where v_{rel} is the relative frequency between the source and observer, and v_{wave} is the speed of propagation of the wave (here, the speed of light). Otherwise, the classical formulae change to follow the tenets of special relativity:

(1) the laws of physics are same in any reference frame,

(2) the speed of an e.m. wave (light) is finite and constant in the same medium regardless of the motion of either observer or source.

Basically you formulate everything in factors of the speed of light, add in the Lorentz factor γ = 1/√1-(v/c)^{2} for time dilation, and you are good to go:

f_{o}/f_{s} = (1-v/c)γ = √[(1-v/c)/(1+v/c)]

In the limit where the relative velocity between the source and observer is much smaller than the speed of light, v « c, this formula reduces to the classical one. For a light source moving away from you, the frequency appears to decrease, the wavelength lengthens and the observed light is shifted toward the red end of the visible spectrum. See the recent post on this wavelength shift in relation to astronomy!

Gabriel's Horn

Gabriel’s Horn is a three dimensional surface that contains a finite volume but has an infinite surface area. It is made by taking the two dimensional graph of y=1/x and revolving it around the x-axis (with the domain of x ≥ 1). If we look at x coordinates from 1 to *a*, the volume can be found by the equation: Which is really just sum of the area of each circular cross section, hence it is the integral of πr

^{2}(with

*r*being the distance from the x-axis to the function). The surface area of the horn can be found by the equation: (Which is slightly more complicated to derive but a full explanation can be found here.) As you can see if we let

*a*approach infinity, the surface area diverges, whereas the volume converges to π.

Vedic Multiplication

(Technically called Nikhilam Navatashcaramam Dashatah) This is a quick and simple way to multiply any two numbers. It’s easiest when the numbers are both close to a power of ten, but it will always work. The first step is to chose a power of ten that the numbers are closest to. In my example I will find the product of 14 and 12. Since 12 and 14 are close to 10 I will chose 10. 14 is 4 more than 10, and 12 is 2 more than 10, so I will write these numbers off to the side, as shown.

+4 times +2 is 8 so I write this number on the right. Then I cross add the 14 and the 2 or I add 12 and 4 to get 16. I write this number to the left, and put these two numbers together to get the right answer 168. (Although I say “put these numbers together” what is actually going on is that 16 is being multiplied by 10 then 8 is added. Knowing this will be helpful when the number on the right is larger than the chosen power of ten.)

Here’s an example with larger numbers. Since they are closer to 100, 100 is used instead of 10. This time the numbers are less than the chosen power of ten, but the same method can be used. Multiply -8 by -11 to get 88 (write that on the right), and add 89 to -8, or 92 to -11 to get 81 (write that on the left). 81 is then multiplied by 100 (since that is the power of ten we chose) and 88 is added. Hence the correct answer to 92x89 is 8188. This is a neat trick, but why does it work? consider the following algebra:

(x+a)(x+b)=c

x^2+ x*a+x*b+a*b=c

x(x+a+b)+a*b=c

Say x is the power of ten we chose. Then a and b are the the two numbers that represent how far our factors are from the chosen power of ten.

[MC integration] Don't you already have to know something about the volume of integration in order to determine if a point inside the hypercube is also in the region of integration?

In this post, we talked about using Monte Carlo methods to evaluate an integral numerically.

The answer here is that you do need to know what your region of integration is. To be clear: MC integration can’t be used to find out what the region of integration is, because that’s your choice! Pragmatically, this region Ω can be defined by bounding functions: if you were integrating on a semicircle, for example, your bounds might be x ∈ [-1,1] and 0 ≤ y ≤ (1-x^{2})^{½}. So you have a way to ask “given the point p, is p ∈ Ω?” But what you don’t have is an easy way to ask about the volume of Ω. The latter functionality is provided by the Monte Carlo process, by comparing the number of points in the hypercube that fall inside and outside of Ω.

In terms of programming, you might “define” the region as a function that takes a point in your domain and gives back a boolean value. The function would basically be (with && as the logical AND operator):

Domain(p) = f_{1}(p) && f_{2}(p) && f_{3}(p) && …

Where f_{i} are your individual conditions (you might have one for each integral, for example, if you’re doing a multidimensional integral); together these f_{i} must be sufficient to determine Ω = { p ∈ **R**^{n} | Domain(p) }.