Author: Santino G.

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)

Conquering flight: Caligula (Part 7)

Santino G.

Poor safety protocols caused the demise of Tiberius. Nothing else. Therefore, when building its successor, I didn’t deviate very far from the original design: It still had the Aeroscout motor, streamlined rudder, and ample surface allocated to the flaps. This blog briefly describes the construction process I followed when building my third 3-channel RC plane, Caligula. If more detail about the build is desired, my previous blog elaborates on the process for Tiberius. Starting with the fuselage, I cut foam board into the shape of a square prism and reinforced the inside with packaging tape. To extend its length, I … Continue reading Conquering flight: Caligula (Part 7)

Conquering flight: The ‘flight’ of Tiberius (Part 6)

Santino G.

Despite having slept only 5 hours the previous night, my mind was incredibly alert. Indeed, the anticipation of flying Tiberius inspired a certain tenacity in my actions that day. Just one week prior, on August 3, I had attempted to rebuke gravity with the maiden flight of my first RC plane, Augustus. Unfortunately, due to both a poor CG and an excessive weight with no commensurate thrust, the warping of spacetime would return my dismissal, leaving Augustus in pieces. Today, however, would be different. Applying my newly-developed engineering habit of iterative problem-solving, I learned everything I could from Augustus’ flights … Continue reading Conquering flight: The ‘flight’ of Tiberius (Part 6)

Conquering flight: Tiberius (Part 5)

Santino G.

Building and testing Augustus taught me many hard lessons, including the importance of the center of gravity’s position, the proper design of a rudder, the consequence of excessive weight, and to name a few. Implementing what I had learned, I set upon constructing another 3-channel RC plane, Tiberius. Lighter, longer and sleeker, its future was promising. This short blog describes the construction process and design decisions I made. For the fuselage, I wanted to avoid the squished square design Augustus had, so while defining each side, I cut lines down the foam board that constitutes the fuselage but made both … Continue reading Conquering flight: Tiberius (Part 5)

Conquering flight: The ‘flight’ of Augustus (Part 4)

Santino G.

Weeks of hard labor have culminated to this moment, I reminded myself. The registration process was frustrating (you can expect a blog on it), but the plane finally earned its numbered sticker. At 9 a.m., my father and I drove to the AMA-certified RC field. It was a cool morning, if memory serves, and was the day Augustus would take its first steps into the air and the pages of history. The notion that this plane was perfectly constructed would be wrong. With a fuselage shaped into a lopsided square prism and the center of gravity out of wack from … Continue reading Conquering flight: The ‘flight’ of Augustus (Part 4)

Conquering flight: Augustus (Part 3)

Santino G.

With the proof of concept finished, the 3-channel RC plane could then be tackled. I meticulously studied successful designs, learned of all the possible wing configurations, and practiced flying on a simulator. Construction commenced. The materials I used were foam board and hot glue; the electronics were a transmitter and receiver, a motor, ESC, and servos. I should clarify, however, that this blog is not a direct tutorial; it simply describes the general process I followed. The first part of construction was the fuselage. For this, I took my foam board and cut in straight lines so that it could … Continue reading Conquering flight: Augustus (Part 3)

The complexity of calculus is only superficial

Santino G.

Calculus provided relief from the two-thousand-year decline in mathematics that proceeded the death of Archimedes. With its tools to analyze motion, change, and infinite series, calculus was a novel interpretation of reality and, to many, impossible to understand. Probably more often than not, students have gone into studying this subject with rumors of its difficulty floating in their mind, and, accordingly, they find it intractable. After years of calculus study, however, I find this widespread impression to be false. I cannot generalize my claim over the entirety of calculus just yet, considering I am still only on Calc II, but … Continue reading The complexity of calculus is only superficial