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31 votes

Applications of High School Geometry

Every time I'm doing carpentry/DIY remodeling on my house, I use so much high school geometry that it makes me chuckle. I've had instances where I need to cut angles to make pieces parallel and used ...
Aeryk's user avatar
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20 votes

Real-life problems involving solving triangles

There are many real-life problems involving solving triangles in "Trigonometry for the Practical Man" by James Edgar Thompson. Here are some from Chapter 5: Problem 1 From the top of a ...
Mike Z.'s user avatar
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15 votes

Applications of High School Geometry

Here's my rant that I gave to my students: You are learning this right now because some of you will need this later in life. You may need this information for your daily job. You may need this ...
abestrange's user avatar
12 votes

Earliest real-world uses of Calculus and Linear Algebra

I want to find what the earliest real-world applications of Calculus were. By real-world application, I mean a device, instrument or technology which made lives better. Let's assume that: Earliest = ...
Pedro's user avatar
  • 1,800
8 votes

Earliest real-world uses of Calculus and Linear Algebra

Maxwell's equations (1861) are a set of coupled partial differential equations. They led to Heinrich Hertz demonstrating radio waves in 1887. Marconi sent messages to British battleships in 1899. I ...
Peter Balch's user avatar
8 votes

Earliest real-world uses of Calculus and Linear Algebra

By real-world application, I mean a device, instrument or technology which made lives better and would have been simply impossible without Calculus or Linear Algebra. In the case of calculus, I don't ...
kjdfhlkdfjh's user avatar
8 votes

Earliest real-world uses of Calculus and Linear Algebra

In the late 18th century, ships leaving Europe for other continents routinely brought with them books such as trigonometrical tables and astronomical almanacs. Those almanacs included ephemerides, a.k....
jpmarinier's user avatar
8 votes

Real-life problems involving solving triangles

I’ve got one very specific answer to this question, because I had to dust off my old trigonometry knowledge just yesterday. I tell it as a real-world use of what I had to learn in school out of left ...
Boldewyn's user avatar
  • 181
8 votes

Earliest real-world uses of Calculus and Linear Algebra

The Mercator projection (1569). This map projection revolutionized naval navigation. The vertical coordinate $y$ depends on the latitude $\varphi$. In modern language, it is the integral of the ...
Gerald Edgar's user avatar
  • 7,607
6 votes

Applications of High School Geometry

The problem here is usually less a matter of ‘I know of no instances where I will use this’ and more ‘I cannot relate things I actually do to the abstract concepts here’. A very large number of things ...
Austin Hemmelgarn's user avatar
5 votes

Applications of High School Geometry

[This may seem indirect, but I want to give you something different, therefore additive.] Nate: For geometry, specifically, I think you have to tell the kids something along the lines of "This ...
guest troll's user avatar
4 votes

Staircase method of small integer addition

I would like to invite anyone with tricks and ideas and feels of what feels comfortable (not just efficient) and, hopefully, fast, to do so. Maybe this is an unpopular answer nowadays, but honestly I ...
Justin Skycak's user avatar
4 votes

Sourcing and verifying calculus applications

I vaguely recall seeing the reference to modeling response in a calculus textbook, probably an edition of Stewart or Thomas. I took part of your question and did a "ChatGPT search." My ...
user52817's user avatar
  • 11k
4 votes

Real-life problems involving solving triangles

Triangulation (Wikipedia link) has a wide variety of real-world uses. As a wildlife ecologist, a particularly fun one I can think of is wildlife radio telemetry (Wikipedia link). In this case, a radio ...
anjama's user avatar
  • 261
3 votes

Earliest real-world uses of Calculus and Linear Algebra

I tried researching it (online, not exhaustively). The earliest I could find for a real technological (economic) benefit of calculus was structural (civil) engineering as early as the 1700s with beam ...
user23961's user avatar
3 votes

Earliest real-world uses of Calculus and Linear Algebra

Maybe Archimedes' figuring out that the volume of a sphere is 2/3 the volume of the smallest cylinder surrounding that sphere? This work was performed some time in the third century BCE.
SoronelHaetir's user avatar
3 votes

Earliest real-world uses of Calculus and Linear Algebra

I'd like to offer you another idea, to look at the question from the Methodology POV. IMHO most of the mathematical/science solution have had some application before they were understood, and then ...
Pirin's user avatar
  • 31
3 votes

Applications of High School Geometry

In general, it makes it more difficult for someone to deceive you. It also lets you better recognize when you're getting a good deal. It helps when you're buying something based on dimensions to ...
DKNguyen's user avatar
  • 149
3 votes

Applications of High School Geometry

Before you cut a tree down, it is quite useful to know where it will land, which requires calculating its height. There are several methods depending on similar triangles, e.g., Wikipedia article. A ...
Joseph O'Rourke's user avatar
3 votes

Applications of High School Geometry

The answer to most "when am I gonna use this" questions is the same. The best analogy that I've heard is a gym. People go to the gym and do bicep curls with weights. Why? Are they ever ...
bta's user avatar
  • 531
3 votes

Real-life problems involving solving triangles

One of the classic problems is have them calculate the height of a building. This can be your school building if you want. Given a tall enough building, or an irregularly shaped building, pulling a ...
slebetman's user avatar
  • 161
2 votes

Applications of High School Geometry

My wife is a quilter. We are constantly scaling shapes, figuring out how much fabric is needed to make something, finding the best way to cut fabric to make a given shape, computing how many squares ...
Ross Millikan's user avatar
2 votes

Earliest real-world uses of Calculus and Linear Algebra

It's easier to say what is not touched by calculus or linear algebra. All physics after Newton involved Calculus. Your touchscreen, for example requires an understanding of capacitance, and simple ...
Steph's user avatar
  • 21
2 votes

Real-life problems involving solving triangles

Squares and hexagons can be decomposed into triangles. This opens up a lot of practical problems that I encounter, such as: What is the largest hexagon that can fit into a circle? (you just need the ...
NuclearFission's user avatar
2 votes

Real-life problems involving solving triangles

A caveat: I work in computer vision, so my perspective my be a little biased by a desire to "evangelize" on a currently hot topic. Students these days spend a lot of spare time looking at ...
Francesco Callari's user avatar
1 vote

Real-life problems involving solving triangles

Most college textbooks for trig have some good problems. (For example, see page 43 of this pdf: https://www.slcc.edu/math/docs/math-1060-oer-trigonometry-textbook-version-2.pdf) (When you get to sine ...
Sue VanHattum's user avatar
  • 21.1k
1 vote

Earliest real-world uses of Calculus and Linear Algebra

Back in Greece long ago around 400 to 200 BC by Eudoxus and Archimedes according to Wikipedia calculating the area under a parabola for instance.
stackoverblown's user avatar
1 vote

Earliest real-world uses of Calculus and Linear Algebra

I nominate search engines. Algorithms like page rank are excellent applications of linear algebra. I also nominate neural networks. Deep learning and neural networks are underneath generative AI, like ...
user52817's user avatar
  • 11k
1 vote

Real-World Problems for Teaching Extrema and Derivative Tests in STEM Education

A Google search showed several that I bet won't satisfy you (fence enclosing, box making). I think you'd have to trawl through a lot of textbooks and look at end of chapter exercises and extract the ...
guest troll's user avatar
1 vote

Applications of High School Geometry

As is fashionable, I talked to my pupils about careers in artificial intelligence. I think they were interested. I will be told that logic that comes into play in AI is not geometry. I'll get to that. ...
Stéphane Jaouen's user avatar

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