The Functions Book Tag!!

I haven’t done a tag in quite a while (I’m sorry) and I think I just kind of forgot what I was tagged for (sorry again)?? But they are really fun, and I definitely want to complete them. I thought this would be a wonderful way to start since it looks quite fun!! Also yes, I am super late to this but uh…ignore that.

Thank you to Naemi @A Book Owl’s Corner for the tag!! Also, the graphics used during this tag are from Naemi, so thank you for that (because I am lazy, and eternally grateful).

The Rules:

• Thank the person who nominated you!
• Ping-back to the original creator, Naemi @ A Book Owl’s Corner, so that she can sneakily read your answers and be thrilled at how much attention math is getting within the bookish community!
• Answer all the prompts while appreciating the mathematical beauty contained in them! (You’re more than welcome to use the original graphics so that all the canva and GeoGebra work the creator put into them will be worth it…)
• Tag some people! Five would be best, since five is obviously the coolest natural number out there, but any other quantity works, too.

Let’s start!

The constant zero function x ↦ 0 maps every number to zero. And although finding its intersections with other functions is one of mathematicians’ greatest obsessions, one can’t deny that the zero function itself just isn’t all that exciting…

For this prompt, pick a book so monotonously boring you almost fell asleep reading it!

Hear me out on this one. I probably just have a vendetta against this entirely because of the fact that it was required reading in seventh grade (with at least fifteen tests on highly obscure moments and vocabulary. No, I do not remember the exact page number that meat was first mentioned! Why is it important that I do?! And oh, so sorry I don’t know what “Demesne” means because knowing that is very important to life overall) and I remember just being bored the whole time. I didn’t enjoy the story, but since many people did, I’m wondering if I’ve judged it unfairly. I pretty much skimmed it, and couldn’t find myself interested at any point in time. I’m tempted to give it another chance to see if I really was biased because of tests and forced annotations (I wouldn’t blame myself), but maybe later when I have less irrational annoyance associated with it.

Also known as the identity map, the function x ↦ x is central to mathematics. Not only is it the most basic linear function in existence, but it also gives certain collections of functions a group structure by functioning as the group’s neutral element: When you compose a function with the identity map, you obtain the same function as before.

For this prompt, choose a book with a generic plot that you can’t help but love!

I think most rom coms would honestly work for this, because while the plot was super predictable, I had a lot of fun reading it!! Also, it has dual POV so who wouldn’t love that?

The graphs of degree-two polynomial functions such as x ↦ x² are called parabolas. When the corresponding polynomial’s leading coefficient is positive, as is the case here, the parabola is symmetrical to a vertical line going through its lowest point, the vertex.

For this prompt, choose a book or series with an epic beginning and ending, but a lackluster middle!

This one honestly had me stumped for a while. I could complain about bad endings for ages, but I don’t think I’ve stumbled upon very many boring middles. That being said, Six Crimson Crane had a plot that didn’t quite grip me till the end. The start had intriguing world building, however as it progressed, the book became too slow paced for my tastes. The last few chapters however, gripped me, and I couldn’t put the book down till I finished them.

The inverse of x ↦ x² on the non-negative reals, the function x ↦ √x assigns the square root of a given number to that number – provided the number in question is greater than or equal to zero.

For this prompt, explore your literary roots and pick a book that got you into reading!

Dork Diaries all the way. I wanted to say Percy Jackson, but that came after. I read quite a bit when I was younger, however the books that made me realize it were Dork Diaries. They were essentially my childhood, and I think I own most of them to this day.

Like parabolas, hyperbolas are conic sections – graphs obtained by intersecting the surface of a cone with a plane. The standard hyperbola is given by the map x ↦ 1/x, the most basic rational function out there.

For this prompt, choose a book with a scenario so unrealistic you can’t help thinking it’s full of hyperbole and over the top!

I have too many for this question. I still love all of them, but the situations are a little over the top. Most books where the love interest is a billionaire CEO of some company, and the main character has a much smaller job do seem highly unlikely (I am there for the romance though) as well as books with extremely lucky characters. There’s a portion of Defy the Night, which I’m not going to spoil, but the entire situation didn’t really make sense in terms of who certain characters had been built up to be, and it felt like a situation with plot armor.

Inarguably one of the most famous functions out there, the sine function x ↦ sin(x), is particularly well known for its characteristically wavy graph.

For this prompt, pick a book that was an emotional roller coaster of ups and downs!

I will not stop recommending this book because I love it so much. Every character was so perfectly done, and the plot was an incredible rollercoaster I’d want to go on again and again. Also for this, Legendborn!! (because i am unable to stick to one book and I’m aware of that fact) My opinions of each characters kept shifting in a perfect way with the plot (not in an annoying nobody makes sense way but a omg layers?? onions?? love that?? way) so I highly recommend both forever.

Although often treated as an afterthought to sine, the cosine function x ↦ cos(x) is meritable in its own right. For example, π, one of the most beautiful constants in the universe, is defined in higher mathematics as twice the first positive zero of the cosine function:

Using this power series, one can show that π is precisely the ratio of a circle’s circumference to its diameter. If that isn’t cool, I don’t know what is!

For this prompt, pick a book featuring pie!

I… do not know of any book featuring pie unfortunately, so I’ll have to skip it.

The quotient of sine and cosine, the tangent function x ↦ tan(x) completes our main trigonometric trio.

For this prompt, pick a book loves to go on tangents so much that it needs footnotes to do them justice!

…I might just be terrible at this because see I don’t think I’ve ever read a book with footnotes?? That I remember, at least. But it also sounds so cool?? I demand recommendations. That I’ll get to. Eventually…

As a function that is its own derivative, the natural exponential function x ↦ e^x is a symbol of absolute mathematical perfection.

For this prompt, pick your favorite book of all time!

…just one? really? must i? because i don’t think i’d know, considering it’s completely dependent on my mood. However, Legendborn has been something I’ve found consistently good, and I didn’t want to put it down, so I’d have to pick it for this answer. ALSO I’M ABSOLUTELY IN LOVE WITH THIS COVER IT IS STUNNING PERFECTION AND I WILL NEVER BE OVER IT.

The inverse of the natural exponential function, the natural logarithm function x ↦ ln(x), sometimes also written as x ↦ log(x), is extremely relevant to anyone studying in a scientific field. We’d have run out of paper long ago without the introduction of logarithmic scales!

For this prompt, choose a book that features logs or journal entries!

Dork Diaries again!! Because while I know that there are probably some incredibly well written and fascinating books written in a journal form, I… gotta stick with the one that is most prominent in my mind.

An example of a fractal curve, the Weierstrass function x ↦ W_α(x) is continuous everywhere but differentiable nowhere. By discovering it, German mathematician Karl Weierstraß was able to disprove the previously popular claim that such functions did not exist, earning the function the moniker “monster”.

For this prompt, choose a book you find truly intimidating!

I actually bought a copy of this as one of the gifts to my sister because see, she like classic literature and I don’t think I understand it. I’ve tried it, however deciphering the difference in dialect makes it hard to lose myself within a story. While this book seems interesting, classic literature as a whole intimidates me at this point, regardless of my goals to read more of it. I think at this point I don’t love it?? But there’s a lot more of it to read! (recs are once again appreciated)

You’re not getting a graph for this one because looking at the Riemann zeta function s ↦ ζ(s) only really gets interesting over the complex numbers… And I’m afraid I haven’t figured out how to plot four dimensionally yet!

However, to say that the Riemann zeta function is interesting is almost an understatement. The Riemann Hypothesis, which claims that ζ has zeros only at the negative even integers and complex numbers with real part 1/2, is one of the biggest open conjectures in pure mathematics. Proving it would earn you both eternal glory and a million dollars’ worth of prize money and be just about the most satisfying thing ever!

(And trust me, I’ve tried. I took an entire course on the zeta function at university in hopes of becoming knowledgeable enough to prove the Riemann Hypothesis, but, if anything, I felt way dumber afterwards than I did before…)

For this final prompt, pick an intriguing book you hope to tackle in the future and are eyeing as your next possible read!

…

OKAY LOOK IN MY DEFENSE. I KNOW I SHOULD’VE READ THIS ALREADY. I KNOW I’VE BEEN SAYING I WILL SINCE I STARTED THIS BLOG, BUT I MEAN IT THIS TIME PROBABLY!! Okay, in all honesty I’ll probably get distracted by another book…but at this point, I’m hoping to read this next!!

I’m leaving this tag open to anyone who’d like to participate!! I would definitely encourage you to, it was highly entertaining to participate in!!

Can this just alternatively be titled “Amaya can’t make decisions for almost 2k words straight”? Yes, yes it can be and it really should be. Thank you once again to Naemi for the tag!! Let me know if we share similar answers, book recommendations, and general thoughts in the comments!! See you next time!!

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