✓ ID #62534

Name: Eliza (middle name)
Age: 17
Gender: Female
Country: India
Type of Pen Pal: Email

Hi, I’m Eliza!
I’m in my final year of high school and kind of stressing out about colleges.
My hobbies include listening to music, buying books I’ll never finish reading and sketching. I’ve recently been really into Asimov and sci-fi. I’ve been trying to get into poetry but I don’t know where to start, I’d love some recommendations.
I absolutely love Tom Lehrer and all his songs so if you get his humour, we’ll get along.
I love TV shows but I don’t watch them a lot, I just don’t have the time anymore. My all-time favourites would be House and Seinfeld.

I really love learning maths, chemistry, astrophysics, quantum mechanics and psychology. I hope to major in pure mathematics in college. I’d love it I could meet a fellow nerd! I might talk about school a lot. I’m also really interested in languages. I speak 3 languages fluently and I’m a beginner at 3 others.

I have social anxiety, it’s difficult for me to talk comfortably with a person face to face, so I don’t have any really close friends. So I’m looking forward to making some good friendships that last! I would love to exchange long emails about our days and thoughts, anything really. I’ve always loved the idea of having a penpal.

I would’ve really loved to snail mail but I’m broke so I’ll have to settle on email.
I’m not really into social media but I spent a lot of time on YouTube, though I’m trying to spend less. I’m a dog person, by the way.
So, if we have some things in common and I seem okay I’d love to hear from you.

Preferences: Preferably between ages 15-20 and female. No homophobes, xenophobes etc. I’d like to meet people from other countries, it’s okay if you’re not though. I also hope you don’t swear too much. And please stay, don’t leave after a while.

2

~23/05/18~

Day 23/31 of the May Study Challenge!! 🍃✨

23. What type of learner are you (visual, kinetic, etc.)? How does this translate to your study methods? Ummm… I’ve never really had a specific type but I guess it depends on the subject - for languages and music, I’m a good auditory learner… for maths and sciences - between visual and kinaesthetic as I like to see practical applications too! ✨

A couple of photos from today - loads of vectors questions and the entirety of year 1 physical chemistry on one sheet of A3 paper!…

EDEXCEL MATHS (Higher Tier) PAPER 1 - KEY POINTS FOR GCSE 2018

Sorry these are shorter! I do need to sleep and couldn’t get them done earlier. There wasn’t much I could think of considering most of my revision has just been practice practice practice but here we are! (Disclaimer: I do not own any of the pictures used here)

• Remember the special angles! They are especially likely to come up on non-calculator as they include showing skills on surds

• When doing proofs, remember to always give reasons for each stage of your working

• When confronted with missing ratios in the form of fractions, percentages etc, always try to make things into a fraction with the same denominator (if possible. I’ve always struggled with these questions so this is helpful for me)

• Don’t be shocked/think your wrong if whatever you’ve simplified ends up as a quadratic! Edexcel likes sneaking quadratics into as many questions as possible!

• Also rememeber the quadratic formula and proof for it - this could also come up on non-calculator!!

• When confronted with a vectors question, always write down the routes! This is usually worth a mark alone so even if you cannot work it out, write this down!!

• If you seriously cannot work something out, at the very least, write something down. Rewrite information given in the question, it can be worth marks!!

• When confronted with a circle/angle theorom question, start working out all of the angles you can. Eventually you’ll reach the right one

• Ways of proving congruence are SSS, SAS, ASA, RHS, AAS

• When given anything with a triangle, remember to think Pythagoras (special angles!!!), trigonometry, sine or cosine rule

• COSINE RULE CAME UP ON THE NON-CALCULATOR PAPER LAST YEAR SO KNOW IT!

• If you are asked for an estimate, round ALL values to 1 significant figure - this includes your answer AND values such as pi (make it 3)

• Read the question carefully. This sounds stupid but if the question asks about perimeter and you give area, you’re gonna feel pretty stupid

• Check your work. By redoing calculations. I cannot tell how many times I have lot silly marks over stupid mistakes because I didn’t check

• When confronted with surds, the best way to simplify and use is when the base surd is the same

Good luck to you all tomorrow! I hope you do well, try to relax! This is what you’ve been working for!!

If one remembers this particular episode from the popular sitcom ‘Friends’ where Ross is trying to carry a sofa to his apartment, it seems that moving a sofa up the stairs is ridiculously hard.

But life shouldn’t be that hard now should it?

The mathematician Leo Moser posed in 1966 the following curious mathematical problem: what is the shape of largest area in the plane that can be moved around a right-angled corner in a two-dimensional hallway of width 1? This question became known as the moving sofa problem, and is still unsolved fifty years after it was first asked.

The most common shape to move around a tight right angled corner is a square.

And another common shape that would satisfy this criterion is a semi-circle.

But what is the largest area that can be moved around?

Well, it has been conjectured that the shape with the largest area that one can move around a corner is known as “Gerver’s sofa”. And it looks like so:

Wait.. Hang on a second

This sofa would only be effective for right handed turns. One can clearly see that if we have to turn left somewhere we would be kind of in a tough spot.

Prof.Romik from the University of California, Davis has proposed this shape popularly know as Romik’s ambidextrous sofa that solves this problem.

Although Prof.Romik’s sofa may/may not be the not the optimal solution, it is definitely is a breakthrough since this can pave the way for more complex ideas in mathematical analysis and more importantly sofa design.

Have a good one!

Greek Alphabet

Α α = alpha

Β β = beta

Δ δ = delta

Ε ε = epsilon

Φ φ = phi

Γ γ = gamma

Η η = eta

Ι ι = iota

Ξ ξ = ksi

Κ κ = kappa

Λ λ = lambda

Μ μ = mu

Ν ν = nu

Ο ο = omicron

Π π = pi

Ρ ρ = rho

Σ σ = sigma

Τ τ = tau

Θ θ = theta

Ω ω = omega

Χ χ = chi

Υ υ = upsilon

Ζ ζ = zeta

Ψ ψ = psi

A short note on how to interpret Fourier Series animations

When one searches for Fourier series animations online, these amazing gifs are what they stumble upon.

They are absolutely remarkable to look at. But what are the circles actually doing here?


Vector Addition

Your objective is to represent a square wave by combining many sine waves. As you know, the trajectory traced by a particle moving along a circle is a sinusoid:

This kind of looks like a square wave but we can do better by adding another harmonic.

We note that the position of the particle in the two harmonics can be represented as a vector that constantly changes with time like so:

And being vector quantities, instead of representing them separately, we can add them by the rules of vector addition and represent them a single entity i.e:

                                                  Source

The trajectory traced by the resultant of these vectors gives us our waveform. 

And as promised by the Fourier series, adding in more and more harmonics reduces the error in the waveform obtained.

       

Have a good one!

**More amazing Fourier series gifs can be found here.