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Thursday, June 11, 2026

Calculator for Right Angles and Hypotenuse

A right triangle is fully defined by just two of its measurements. Enter any two known values, such as sides or angles, into the calculator below and it will instantly calculate everything else: the hypotenuse, both acute angles, the altitude from the right angle to the hypotenuse, area, perimeter, and the radii of both the inscribed and circumscribed circles.

Right triangle calculator — enter any two side or angle values to compute all triangle properties

Right triangle calculator

Enter any two known values (sides or acute angles) to solve all properties.

For information on other tools and topics:

Tuesday, June 02, 2026

Trail Walking with a Say's Phoebe

 

A bird that appears to be a Say's Phoebe was jumping from fence post to fence post ahead of me and Joie while we walked, until it finally flew onto a nearby bush, on a Mid-Spring morning. It kind of seemed like they wanted us to follow, but maybe they were just keeping an eye out for any bugs we might stir up as we walked along the trail, a behavior for which Flycatchers are known.

Instagram: https://www.instagram.com/p/DZBUlwADrIJ/

Sunday, May 31, 2026

Auckland Exploration on Te Ika-a-Māui

After over a full day's delay, we finally landed on North Island of New Zealand in Auckland a bit late in the day on December 8.  After settling in, Allie and I took a running start on December 9 for our exploration of the city.  Sky Tower is within walking distance of our hotel, so we headed over. Sky Tower is tall enough to view everything in Auckland from high-up. Many of the places we will be exploring are clearly visible.






After getting-the-lay-of-the-land, we explored on foot for while, then had an awesome dinner at Origine Bistro with great food and incredible service.  We had a table that offered a good view of the Harbor too.


 

 


Due to the delay in arrival, there are a number of places we had to push off or reconsider for another trip in the future. However, the next few days did not disappoint!

Wednesday, May 27, 2026

Unfortunate Extra Day in Queenstown

 After enjoying a few days in Queenstown and surrounding region, we were excited about travelling to Auckland on December 7, 2026.  We took the morning easy in preparation for our flight to Auckland. Unfortunately, our flight from Queenstown was cancelled due to high winds after we arrived at the airport, and after we checked our bags and went thru security. So we had to retrieve our checked bags and find overnight accommodations. I found a room at the Hilton Queenstown Resort. We were reassigned a flight the next morning.

After we checked-in to the hotel, we took the water taxi to Queenstown CBD for a late lunch at a great seafood restaurant, and some ice cream at a popular shop. We then roamed a bit around the touristy area before returning via water taxi to the hotel for the evening.

At some point during the night, the reassigned flight was also cancelled. We were forced to accept an even later evening flight. In turn, this forced me to start cancelling plans in Auckland, as we were losing a day in town.

Lost Day - December 8, 2026

We didn’t plan for anything in Queenstown on this day, due to it being a lost day. We had breakfast at the hotel cafe, but otherwise relaxed in the hotel room until checkout time.  We finally went to the airport in the afternoon to wait for our early evening flight.

This flight was not cancelled. 

We ultimately landed in Auckland in the evening. After taking our hired towncar to the hotel and checking-in, we settled a bit then went to the hotel cafe for dinner.  Due to our delayed arrival, we had to rearrange plans for our first day in Auckland.

Monday, May 25, 2026

Queenstown New Zealand Exploration

Allie and I arrived in Queenstown on December 3, 2026 in the afternoon (local time). We left California our previous day of December 1, 2026 (local time). We lost a day to travel and another day to the International Date Line. We also lost a portion of one day to a long stay in Auckland Airport on our way to Queenstown. The following are my journal entries from the first few days.


Tuesday, December 3: A Lakeside Welcome at Wakatipu Grill

We stayed at the DoubleTree by Hilton in Kawarau Village near Queenstown. After settling in, we walked over to Wakatipu Grill at Hilton Queenstown Resort and Spa. Restaurant staff sat us in a glass-enclosed patio with good views of the lake as the sun set. The dishes were very good. I had the Pork Porchette, and Allie had a steak dish she liked a lot. We also tried a drink called a Matcha Mojito, which ended up tasting more like a Long Island Ice Tea than anything that should bear the name “mojito” or “matcha.”

The staff were really helpful, though. They went out of their way to make an actual Iced Tea for me even though it’s not on the menu. For a location that doesn’t brew iced tea, they made a great one. Dessert was a bit of a surprise. The Strawberry Cheesecake was really more of a strawberry mousse. Even still, it was fairly tasty, just not what we expected. We also had a type of Chocolate cake that tasted very good but came with a super hard chocolate shell that was thicker than a candy bar. It literally required a steak knife to break through. The shell was likely just too thick, making it a bit of a nuisance to an otherwise tasty dish. Overall, it was a great experience with extremely attentive, capable staff.


Wednesday, December 4: Water Taxis, Gondolas, and Queenstown CBD

The weather was nice and sunny with light cloud cover and a little bit of a morning chill. We started the itinerary by taking a water taxi from the Hilton over to the Queenstown CBD, which let us see the area from the lake and take in the gorgeous scenery. From the CBD, we walked over to the Skyline Gondolas. On the ride up to Skyline Queenstown, we saw and heard a goat on the side of the mountain. I had an 11:45 reservation at the Stratosfare Restaurant for their buffet lunch. The food was high quality with a lot of great options, and our table offered awesome views of the town and lake from a high vantage point.



Afterward, we hit the souvenir shop before heading back down. We had another appointment at Kiwi Park Queenstown where we explored this special kind of zoo. Highlight is that we were able to catch glimpses of actual kiwi birds! That was awesome. We also saw many other beautiful and native animals, including a bird and reptile show. There was also a happy and buzzy bee colony.




We left the park and roamed around the CBD for some more shopping. The town is very much a touristy place, and there didn’t seem to be a ton of local personality beyond the architecture and the beautiful deep valley lake backdrop. After a long day, we took the water taxi back to the hotel to relax and rest for the evening.


Thursday, December 5: Hiking Frankton and Finding the Local Spots

Allie and I went on an exploratory hike into the Frankton area and ended up at Pantry by Frank’s. We ordered a couple of bagel sandwiches, but what’s called a “bagel” here is more of a white bread with a pastry crust than an actual dense bagel. Allie’s Pesto Chicken sandwich was served cold for whatever reason, while my Chicken Club was warm. Allie had a hot breakfast tea, and I had a hot Chai tea. Exploring the area further, we discovered an Asian market, a grocery store, a very nice laundromat, and a few other shops. The grocery store had a permanent resident cat who guards the entrance as it naps throughout the day. On the way back to the hotel, we took a heavily vegetated trail along the river. The bugs annoyed Allie, but luckily none bit her.

Being so far South on the Globe in the summer means there is still direct sunlight on the city at 9pm. Later that night, I caught a view of the full moon with its light reflecting perfectly across the lake.

On December 6, we took a day-long tour of various Lord of the Rings filming locations on the South Island.  Unfortunately, we had a series of cancelled flights on December 7, so we ended up staying an extra day in Queenstown, not making it to Auckland until December 8.

Sunday, May 24, 2026

Discoveries across the Galaxy

While exploring the Galaxy recently, I made several incredible discoveries.  This first image was taken in a newly discovered system of a white dwarf (DC) as the primary star with closest planet being an Earth-Like World (ELW) and the second planet being Water World (WW). Both planets are under 60ls from their star. This is a very rare configuration, even taking into account all white dwarf types in the Elite Dangerous galaxy. 


In another Neutron Star System, I discovered a rare luminescent lifeform.


On the same trip, I also discovered even rarer Crystalline Shards.

Related Instagram post: https://www.instagram.com/p/DVxR0Y2Dt_j/?img_index=1

Saturday, May 23, 2026

Escape Velocity Calculator

Escape velocity is the minimum speed an object needs to break free from a body's gravitational pull without any further propulsion. The formula is simple: v = √(2GM/r), where G is the gravitational constant, M is the mass of the body, and r is the distance from its center. The result tells you how fast something must be launched to escape that gravity well entirely with no engines required after the initial push.

It can be surprising as to how much this number varies.  Earth's escape velocity is about 11.2 km/s. Jupiter's is over 59 km/s. The Sun's surface escape velocity is around 617 km/s. And for a neutron star, it can be a significant fraction of the speed of light. Use the calculator below to explore escape velocities for planets, stars, galaxies, and any custom body you wish.

Escape Velocity Calculator


For information on other tools and topics:

Friday, May 22, 2026

Movies I watched in the theater in 2017

I am not sure where I saw most theatrically released movies in 2017. This list is put together from memory. One fact I remember is that the only reason I saw Star Wars: The Last Jedi was because The Disaster Artist was sold out when I arrived at the theater. I think this may have been the point where I stopped doing walk-ups and started to regularly buy my seats ahead of time.

Movies I saw in the theater in 2017:




Tuesday, May 19, 2026

Many Paths of the Collatz Conjecture

The Collatz Conjecture is one of mathematics' strange unsolved problems. The rule is deceptively simple: take any positive integer, and if it's even divide it by 2, if it's odd multiply by 3 and add 1. Repeat this process and the sequence seems to always eventually reach 1. Always. This is true for every number ever tested! Even still, no one has ever been able to prove it, though some attempts have got close.

The sequences themselves are practically unpredictable. For example, the number 27 takes 111 steps while rocketing up to 9,232 before finally collapsing to 1. Nearby numbers can reach 1 in just a handful of steps, while others take hundreds of chaotic steps before converging. Use the interactive math tool below to explore and compare up to 5 numbers at once.


Collatz Conjecture Visualizer

Pick any positive integer. If it's even, divide by 2. If it's odd, multiply by 3 and add 1. Repeat. No matter what number you start with, the sequence always seems to reach 1, but nobody has ever proved why. Enter up to 5 numbers to compare their paths.

Enter Numbers to Compare

About the Collatz Conjecture: Mathematician Paul Erdős said: “Mathematics is not yet ready for such problems.”

For information on other tools and topics:

Monday, May 18, 2026

Movies I watched at the theater in 2018

2018 was likely the year I really started using my AMC membership. At some point that year I joined the AMC Stubs program and later upgraded to AMC A-List. Before then, I had never used an elevated membership to go to the movies. I think I had the equivalent of the free Insider level since 2016 or 2017, but I was not using it regularly during those years. Since 2018, I have watched most of my movies at AMC, though not all. For example, I saw Mandy at an independent theater.

Here's the list of movies I was in 2018:




Friday, May 15, 2026

Movies I watched in the theater in 2019

The year was 2019. This was arguably the peak year for going to the theater to see movies. Even still, I saw a surprising 33 movies. That's more than one movie every two weeks!  I was definitely using my AMC A-List membership to its fullest. This was a great year for quality of  movies too. I don't remember trying hard to justify my membership by seeing a bunch of movies just because I could see them for free. There was simply a lot of movies I wanted to see at the theater!

Here is the list of what I watched at the movie theater in 2019:







Thursday, May 14, 2026

Movies I watched at the theater in 2020

It is 2026, but I am going to look back at the movies I actually saw at the theater in 2020. That was a tough year for movies, of course. Even still, I ended up going to the theater a bit more than one might now guess. I really started to use AMC A-List in the prior year, but clearly it did not get much use when everything shut down in 2020 and the program was suspended. I actually watched Tenet at a local drive-in.

Tuesday, May 12, 2026

Movies I've seen in 2025 and "why"

Has there been a return to form for movie theaters to pre-pandemic levels? No. However, I found myself going to the cinema more in 2025 than in 2024. The nature of movie-going has fundamentally changed with the dominance of streaming. Patrons now see fewer films in theaters, opting to wait for many of them to arrive at home. This is especially true for movies not designed as a spectacle or an event, creating a fresh challenge for the industry. Still, theaters have faced similar hurdles before, such as when televisions became commonplace in the home.

Eventually, theatrical films improved after over a decade of adjustment throughout the 1950s and 1960s. Even before then, patrons had stopped attending theaters for short serial shows. Additionally, the concept of made-for-TV movies eventually emerged, allowing lower-quality films to be released directly to television without a theatrical run.

Later, both theaters and television were challenged by the introduction of VHS and movie rentals. This led to the straight-to-video concept for lower-budget films, which raised the quality expectations for theatrical releases even higher.

Today, streaming poses yet another challenge. Many high-quality movies do not necessarily require a theater because they do not rely on spectacle to be enjoyed. Even when a large screen might enhance the experience, a story may be perceived as small scale, making it easier to wait for a streaming release.

Despite all of that, I still enjoy seeing various types and scales of movies at the theater. Some films are so massive they demand a theatrical viewing, such as the Avatar franchise. Others are enhanced by the cinema experience even if they have a straightforward story, like Last Breath.

Finally posting my 2025 list

I have been putting off this post for five months for a simple reason: I saw too many movies in 2025 to make this article enjoyable to create while including a poster for every film, such as last year's article. I believe movie posters add value and enhance the post, but including all of them is an immense amount of work. To that end, I am scaling down this year's post to a simple hyperlinked list.

Here is the list of what I watched at the movie theater in 2025:





Thursday, April 02, 2026

Reaching the known Universe and Project Hail Mary

 

The movie Project Hail Mary touches on a topic about which I recently wrote. That being the ability to reach any point in the Universe within a human lifetime using relativist travel. Time Dilation Visualized is an excellent video that helps visualize both the movie itself and the general discussion as well. Have fun watching and reading about this fascinating exploration.

Thursday, February 12, 2026

Will the Gaming Industry Change Use of FPS and TPS?

The Inertia of Familiar Language 

The traditional definitions of first- and third-person games rely on camera placement rather than on player agency. That shortcut has distorted how we talk about perspective for decades.

So why has this never been corrected?  The short answer is likely inertia.

Once a term becomes familiar, widely taught, and commercially useful, it stops being descriptive and starts being infrastructural. Changing it becomes expensive, not just financially, but culturally.


The FPS Effect

The modern taxonomy of game perspective crystallized in the 1990s with the rise of the first-person shooter (FPS).

“FPS” was an unusually successful label:

  • It described what players saw

  • It differentiated a new genre

  • It was easy to market

  • It spread quickly through magazines, retail shelves, and early web discourse

Once first person became synonymous with “camera at eye level,” everything else was forced into contrast. The term third person did not emerge from narrative theory. It emerged as whatever FPS was not.

This asymmetry locked the vocabulary in place before anyone had reason to question it.


Camera Language Is Easier Than Agency Language

Camera placement is concrete. Agency is abstract.

It is far easier to say:

The camera is behind the character

than to say:

The player issues commands to a represented self

Marketing departments, tutorial writers, and reviewers naturally gravitated toward the simpler explanation. Over time, that simplification hardened into definition.

Once perspective was taught as a visual property, revisiting it as a player–system relationship required more effort than most discourse was willing to invest.


How Designers Commonly Talk About Perspective

In public-facing discourse, perspective is usually described in terms of camera placement. In design-facing discussions, however, the vocabulary often shifts.

Designers frequently frame perspective through concepts such as:

  • Player embodiment

  • Identification with an avatar

  • Degrees of abstraction

  • Command versus inhabitation

  • Latency between decision and action

These ideas appear regularly in design talks, postmortems, and critical writing, even when the traditional labels of first- or third-person remain in place. The emphasis is less on where the camera sits and more on how the player relates to what they control.

This does not mean designers uniformly reject camera-based terminology. Rather, it suggests a practical distinction: the internal language of design often exceeds the precision of the public labels used to describe games.

In other words, the mislabeling persists not because designers lack conceptual tools, but because those tools are rarely surfaced in player-facing taxonomy.


Why the Industry Is Unlikely to Fix the Labels

Even if the argument is sound, several forces resist change:

1. Legacy Vocabulary

Decades of books, articles, reviews, and tutorials use the existing terms. Revising them would create friction with historical material.

2. Search and Discovery

“Third-person action game” is a deeply indexed phrase. Replacing it would damage discoverability without offering immediate commercial upside.

3. Audience Expectations

Players already believe they know what these terms mean. Correcting them risks sounding pedantic or confusing, even when accurate.

4. Mixed Perspectives

Many modern games blur categories intentionally. Studios may prefer flexible ambiguity to precise taxonomy.

Taken together, these pressures make formal correction unlikely.


Why This Still Matters

If the industry is not going to change its labels, why insist on the distinction at all?

Because language shapes analysis.

Mislabeling perspective:

  • Obscures why certain games feel immersive despite external cameras

  • Confuses discussions of agency and control

  • Flattens meaningful differences between avatar play and command play

  • Makes serious criticism sound mystical rather than structural

A player-centric model gives critics, designers, and players a sharper vocabulary—even if public-facing labels remain unchanged.


The Value of a Parallel Vocabulary

This series is not a call to rename genres overnight. It is a proposal for a parallel framework that can coexist with existing terminology while offering greater precision.

Just as film studies distinguish between camera angle and narrative voice, game analysis benefits from separating:

  • What does the camera do

  • What is the player

Keeping these concepts distinct allows deeper discussion without breaking compatibility with established language.


A Useful Mental Reframe

Rather than asking:

Is this game first person or third person?

Ask:

Who is acting?

Who is being addressed?

Where does the player exist in relation to the system?

These questions remain valid regardless of genre, technology, or trend.


Keeping It Going

The industry is unlikely to abandon camera-based labels. They are too entrenched, too useful, and too familiar.  But clarity does not require replacement. It requires recognition.

We can say that a game has first-person perspective with third-person camera angle. Or, a game is second-person perspective with the ability to show either game-piece camera angle or top-down third person camera angle.  Such descriptions are more meaningful. 

Once we understand that most so-called third-person games are structurally second-person, a great deal of confusion dissolves. Design intent becomes clearer. Player experience becomes easier to articulate.


Also see

Tuesday, February 10, 2026

Full Day Lord of the Rings Mavora Lakes Adventure

Allie and I enjoyed an adventure on South Island of New Zealand (Te Waipounamu) where we retraced the steps taken to film Lord of the Rings trilogy. We toured with Trails of Middle Earth on their Full Day Lord of the Rings Mavora Lakes Adventure.  The tour included multiple filming locations for Lord of the Rings in the general Mavora Lakes region, including the famous Orc Mound, Anduin River and Nen Hithoel.[1][2] At Mavora Lake, we had a chance to cosplay with Hobbit outfits and authentic replicas of many battle weapons from the Trilogy. Overall experience was positive.

However, while visiting these filming locations was great, the travel between them is a bit rough. This is the nature of travelling around the South Island of New Zealand in this region, especially when you are leaving paved highways behind for a time.  The tour length definitely adds to discomfort as much as the roads themselves since this is a 10 hour tour, with long stretches between locations.  Just be prepared.  One bit of advice is to pack your own lunch, as I found the location where food was available to purchase to be rather lacking.

 

 






Besides the thrill of discovering so many filming locations in one tour, we also got to see much of the beauty of South Island's mountains and lakes. It feels like New Zealand was always meant to be the location of Middle Earth.