“Up until now we’ve been doing all the easy stuff. Now it is time to cry.”

—
Calculus professor

mathprofessorquotes

*Follow*

“Up until now we’ve been doing all the easy stuff. Now it is time to cry.”

—
Calculus professor

mathprofessorquotes

Normal brain (on left) compared with the math brain (on right). Of course there are a pretty big amount of nuances and combinations to this scheme, and a mixed brain should be the most common type.

scienceisbeauty

Experimental Psychedelic: Tree of Life 2

jakeronomicon

" Warning: Alcohol and Calculus do not mix. Don't drink and derive. "

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चुंबकीय क्षेत्र

magictransistor

i like drawing paradoxical stuff

vambrace

best-lovequotes

Ah, **fractions**. The cornerstone of 4th grade math. Why is it so hard to get our little heads around **fractions**? In math a fraction is simply a way of describing a part of a whole. The Latin origin is helpful: the word **fraction **entered English in the 14th century from the Anglo-French word *fraccioun*, which came from the Old French *fraccion*. The Late Latin word *fractionem *meant *a breaking* and came from *fractus*, the past participle of *frangere *meaning *to break something into parts*. Here is where it gets interesting. Yes, the English words *fragment *and *fracture *share the same roots, entering English around the same time. The Proto-Italic root* *frang*- came from the Proto-Indo-European **bhreg*- meaning *to break* (and root for the word *break*) but also Old English *brecan *meaning *to break*, Lithuanian *brasketi *meaning *to crash* or *crack *and Old Irish *braigim *meaning *to break wind*. Yes, all things 4th grade eventually make their way back to **breaking wind**. A fraction, then is just a part broken off from a whole. That wasn’t so hard, was it? Now, who farted?

kidsneedscience

Experimental Psychedelic: Tree of Life 3

jakeronomicon

Mathematics

*Cont’d from “Kinematics example”.*

This post is best viewed on my blog, click here to be taken to its permalink.

Different problems involving kinematics often share common properites which can be used (or not used) depending on the scenario. Once you become more adept at solving these problems individually, you’ll begin to easily recognise situations where some conditions apply and others may not and start to adapt the conditions to fit the scenario. A bit of thought is required to decide logically whether one condition may be physicaly viable in the situation or not.

In this post, I will look at topics that are not strictly kinematics but have applications within the field and in wider mechanics.

**Boundary conditions**

There are some common boundary conditions (i.e. what happens at the extreme-most points of the motion) which come from logical reasoning.

For motion of an object with its weight perpendicular to flight motion it can be assumed that the *x*-component of velocity stays constant throughout the flight. This means that the final *x*velocity, *v** _{x}*, is equal to the initial

Themaximum height of flight, *y*_{max},is always the point where the *y*
velocity, *v _{y}* = 0. This is
a direct result of calculus, wherein

Additionally,
if we set the original position of the object at the origin of our system of
co-ordinates, the point at which we find it at the same height again (the point
where it lands, assuming it lands at the same height) by setting *y* = 0.

From there we can select an appropriate SUVAT equation.

**Forces and vector resolution**

*See “Resolving vectors”***.**

Sometimes you may have to combine energy conservation, momentum or force superposition (mostly, for equibrium) into your answer.

Now, if
something is accelerating then its vectorial sum of all forces is equal to *m***a**,
where **a** is its resultant acceleration. If it is in equilibrium (“stationary” or “moving at constant velocity”) then the
vector sum of its forces is equal to zero. This is a very important consequence and can be used extensively to solve problems.

You
should always remember to resolve *all* forces/vectors in a free body
diagram when working on the *x* and *y* components separately. Unless
a vector is at 90° from the direction you’re
resolving it to it will contribute that component. For example, the vector **W** acts *only *in the *y*-direction, meaning
we can leave it out of our *x*-component
resolution.

Remember,
if a vector points in the opposite direction to the direction you’re working
in, give its magnitude a negative sign. This is what’s intended by the *vectorial* (or algebraic) sum as opposed
to a simply scalar summation.

**Resistive forces and their
applications**

*See a question about friction*.

Generally,
in kinematics we ignore the effects of resistive forces – especially air
resistance – since they can make problems more complicated to solve. However,
resistive forces such as the friction force **F _{f}** or the reaction force

The magnitude of the frictional is given by

F=_{f}μR,

where *μ*
is the friction coefficient. Vectorially, we define **F _{f}** to be perpendicular to the reaction force

F= −_{f}μR,v

although the magnitude will usually suffice.

Now, we
shall further examine what is meant by the reaction force. The reaction force
is defined in a direction perpendicular to the surface the object rests upon
and will often have its *y*-component *R _{x}* equal in magnitude and
opposite in direction to the weight

R=_{x}W,

assuming the object is fully supported by the surface it sits upon.

These results can be useful when applied simultaneously. If we know the frictional force and friction coefficient, we can find the reaction force and, in turn, the object’s weight. Since we know that

W=mg

from Newton’s second law of motion, we can
hence find the object’s mass and its overall acceleration.

physicsandchemistryrevision

mathwork

I should probably stop now. It’s 11:20 pm and I’ve checked 10 out of 18 of the things I had to do this weekend. Today I studied: • History (Middle Ages) • Chemistry (Periodic Table properties) • Algebra • a bit of the SAT’s writing section I guess it was a pretty productive day! oh and I downloaded that tree app and it’s so good that I actually felt bad for killing the tree. /February 28th 2015/

yourstudygroup

“The idea behind math is that it’s an idea; numbers are an idea. And really you do have to have faith to believe in the concept of numbers. It’s interesting to see patterns everywhere.”

—
Lacey Sturm

laceysturmquotes

Experimental Psychedelic: Tree of Life 5

jakeronomicon

I think that mathematically interested sixth formers, wanting to study the subject at University, should have some background knowledge. Many would have heard about the Riemann Hypothesis and a link to prime numbers; this subject is beyond the scope of this blog but school pupils, with knowledge of prime numbers and geometric progressions, can see how the Zeta Function relates to prime numbers in the above bit of mathematics. I like it anyway.

jpedmaths

Doing math with some natural light! I never realized how much I do math until I started posting pictures of my un-colorful work. T_T

weheartonepiece

//28-02-15/13:22// Math study guide manufacturing is going smoothly and I am using my new pens!!

mymotivationtostudy

Julia 1

jakeronomicon

2 hours of math + no paper left

livingonmarsnotonearth

msistriggerwarning