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Introduction

Santino G.

print(“Hello, world!”) I am a high school student who is passionate about engineering, math, coding (hence the “Hello, world!” reference), space, and more topics than I have time to study. The goals of this blog are the following: catalog all my projects in one place, develop the skill of communicating complex topics in simple terms, find gaps in my understanding of subjects, and use this blog as a forcing function for swift project completion. If you have found this blog, you are probably a college that is interested in my portfolio. Hopefully, you enjoy it. I will attempt to maintain … Continue reading Introduction

Regulatory hurdles in my model rocketry hobby

Santino G.

To regulars of this blog, long elaborations of radio-controlled (RC) plane failures ring a familiar tone. While much of my free time is indeed spent in such endeavors, there is an additional hobby of mine that I have barely discussed and yet has successfully consumed most (if not all) of my leftover leisure: model rocketry. This isn’t by accident, of course. There is very little to write about due to regulations preventing my procurement of a launch site, something that’s sort of necessary to have. Here, I collate some of the frustrating processes I have undergone in hopes that someone … Continue reading Regulatory hurdles in my model rocketry hobby

Orthogonal projections in linear algebra

Santino G.

In linear algebra, we are occasionally interested in resolving vectors into their “projections.” In contrast with components, however, which are determined with respect to the x- and y-axis, projections are determined with respect to an adjacent vector, one that shares the same initial point. This blog discusses the derivation of formulas that help us in finding these projections. Suppose we have two nonzero vectors u and v in 2-space. The vector u can be written as a sum of vectors, say, and : (i) where is constructed to be parallel to the adjacent vector v and is made to be … Continue reading Orthogonal projections in linear algebra

Conquering flight: The flight of Claudius (Part 10)

Santino G.

The temperatures have continued their gentle decline as planet Earth’s geographic north pole has strayed farther and farther from the sun. Nevertheless, the warmth provided by sweaters and experimental aircraft kept all of us comfortable that morning. Indeed, with the confidence I felt in the upcoming flight, I might have mistaken the season as spring. Embarking soon after sunrise, we arrived in step with the large morning attendance and immediately started to unload the newest iteration of the 3-channel RC plane. With its new weight-reducing features, Claudius was the lightest aircraft I had ever built. Some notable improvements were the … Continue reading Conquering flight: The flight of Claudius (Part 10)

Conquering flight: Claudius (Part 9)

Santino G.

One problem has pervaded all of my previous RC planes: weight. While I have been trying to minimize this one parameter in every plane since Augustus, it was only after I flew my third RC plane, Caligula, that I understood a more aggressive approach was necessary. This blog describes the construction of my fourth 3-channel RC plane, Claudius. Beginning with the fuselage, I maintained the same design used on the previous two; that is, foam board cut and folded so as to feature a square cross-section. It was, however, slightly shorter than Caligula’s. (This wasn’t an intentional decision; I simply … Continue reading Conquering flight: Claudius (Part 9)

Some physics pertaining to model rocketry

Santino G.

Despite my earnest pursuit of the model rocketry hobby, my efforts have been continuously undermined by the lack of one seemingly trivial thing: a launch site. This blog will not be focusing on this regulatory struggle (though, that would make a good post). Instead, I will collate some of the interesting physics I have learned regarding model rockets. The reader may rest assured, however, that my posts about my RC plane hobby will continue shortly. (Claudius is the next plane in construction and should be lighter than Caligula, Tiberius, and Augustus.) Center of mass (CM), center of gravity (CG), and … Continue reading Some physics pertaining to model rocketry

The fundamentals of Java

Santino G.

Being an object-oriented programming (OOP) language, Java has a substratum of classes and objects set as its foundation. This blog will briefly describe these two concepts. Classes In order to describe a real world object in our program, we start with a generalized version of it, a version with all of the attributes and behavior of the thing, but without any specific values. In Java, we call this uninitialized object a class. You can think of a class as a blueprint. For instance, when planning the construction of a neighborhood, a contractor will design a handful of designs for the … Continue reading The fundamentals of Java

Cross products and dot products in linear algebra

Santino G.

This is a short post where I briefly describe cross products and dot products. If you have not previously studied linear algebra, the math may be a tad complicated. Cross products The cross product of two 3D vectors u and v () defines the components of the vector that is orthogonal (perpendicular) to both. That is all! Quite simple. The formula is similarly intelligible. For vectors and , their cross product would be A better way of writing this would be in terms of determinants as so This formula can be remembered by considering the 2×3 matrix whose first row … Continue reading Cross products and dot products in linear algebra

The state of the RC hobby

Santino G.

Over the past four months, I have been designing, building, and flying radio-controlled (RC) planes. While many of my blogs regarding this topic focus on the construction and testing of these model aircraft, this blog summarizes the progress I have made and future plans I have. Essentially, this will reflect on the state of my RC hobby. Augustus… Named after the first emperor of Rome, this plane was flawed by the following: Being my first 3-channel model aircraft, mistakes are likely to abound, but the lessons were directly proportional with these. As for Augustus’ flight, this photo says it all. … Continue reading The state of the RC hobby

Novel interpretation of the Delta-Epsilon Proof (maybe)

Santino G.

While writing my calculus blog, I found (perhaps even discovered) a new way of thinking about the – (delta-epsilon) proof. This interpretation won’t cause any kind of epistemic revolution in mathematics, but I believe it’s a helpful pedagogical tool worthy of its own blog post. In case you have forgotten, the limit definition states the following (where and are real numbers): To prove a limit statement, we have to show that the limit satisfies this definition. How do we do this? We assume exists and show that, no matter what the value of is, there exists a corresponding . The … Continue reading Novel interpretation of the Delta-Epsilon Proof (maybe)

Conquering flight: The flight of Caligula (Part 8)

Santino G.

Although the construction phase of Caligula ended in late August, its flight was grounded for multiple weekends by bad weather and packed schedules, thereby pushing its launch all the way into the middle of September. With both the atmosphere and our timetables aligning on a cool Sunday morning, we set out to the field in hopes to witness the successful flight of my third RC plane, Caligula. When we arrived at our local RC club’s runway, we were immediately greeted by the corn’s fall colors as well as by a couple of seasoned hobbyists who were eager to look over … Continue reading Conquering flight: The flight of Caligula (Part 8)