Questions tagged [geometry]

For questions related to geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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9
votes
2answers
225 views

Teaching geometric transformations through fractals?

In roughly two weeks, my secondary geometry class will have reached the part of the year where we discuss geometric translations: translation, rotation, and reflection. Dilation i am going to use as ...
8
votes
0answers
179 views

Moore method projective geometry

Has anyone written a set of Moore method notes for synthetic projective geometry? It seems like it would be well-suited, but I haven't been able to find any such thing on the Internet.
12
votes
5answers
524 views

Geometry with a view towards differential geometry textbook

I am scheduled to teach an upper-division undergraduate class on "Geometry" and I get to choose more or less what that means. Common choices seem to be non-Euclidean, hyperbolic, projective, or ...
9
votes
5answers
198 views

Extensions beyond Euclidian Geometry for Secondary students

My secondary geometry class is really amazing and is likely going to finish everything I have for the curriculum with a few weeks left in the school year. I was thinking to use these last few weeks ...
39
votes
35answers
15k views

Real-world examples of more “obscure” geometric figures

As part of my secondary geometry class I like to hook students by presenting real-world examples (usually images I find online or have taken myself) of different geometric shapes from real life. For ...
3
votes
3answers
1k views

interesting/challenging geometric constructions for gifted secondary students

I have three students in my secondary geometry class that just destroy everything I throw at them. I tasked them with writing the word problems for their midterms and one of the three wrote simply "...
18
votes
10answers
5k views

A parabolic arc is not semicircular. But students think so

I'm teaching a Calc 2 class now (integration and applications) and I'm surprised that more than a handful of students seem to think the graph of $y=x^2$ on $-1\le x\le 1$ is part of a circle! Here is ...
12
votes
4answers
457 views

Is there an elementary way to explain that a map of the earth cannot preserve distances?

I am teaching a short "topics in geometry" course to future high school math teacher in France. I plan to cover some spherical geometry. I will be treating the following topics: volume of the ball ...
33
votes
16answers
10k views

Why are triangles so prevalent in high school geometry?

A colleague and I recently discussed what we call the "Triangle Trap." High school geometry covers a very large unit reflecting the common core: Classifying Triangles Triangle Angle Properties ...
10
votes
2answers
1k views

Project/Assessment based on Flatland for Secondary Geometry Class

One of my favorite books is Flatland by Edwin Abbott, which is incredibly rich in geometric concepts especially relating to dimensionality. I would really like to assign it to my secondary geometry ...
7
votes
4answers
3k views

How Can I Motivate Geometric Constructions?

When starting compass and straightedge geometric constructions in my grade 8-9 maths classes, I usually begin by mentioning a little about Euclid and the fact that constructions have been done for ...
8
votes
2answers
3k views

Notation of points with coordinates

At least in Germany, nearly all teachers and textbooks use the notation $$P(x,y)$$ for the point $P$ with coordinates $x$ and $y$. My own math professors at university always cried about this, as the ...
19
votes
4answers
990 views

Teaching manifolds to high schoolers

I would like to introduce the concept of a manifold to a high school student. This person isn't familiar with the axioms of set theory nor topology. However, despite these deficits, I would like to ...
18
votes
12answers
8k views

How to explain that we live in a three-dimensional world?

How does one explain, clearly and simply, that we live in a three-dimensional world? The explanation has to be understandable for a twelve year old child.
11
votes
4answers
261 views

Helping students use constructions in geometry

I work as a teaching assistant in a high school and geometry gives most students headaches. I emphasize understanding the problem by constructing lines and using elementary properties to arrive at ...
4
votes
7answers
955 views

Fun Activities/Games Before a Break/Between Units for Secondary Geometry

I have been planning ahead and it looks like i will have a solid three to four days before the winter break where we wont really be in a unit. We will have just finished a unit and i do not want to ...
9
votes
4answers
1k views

Secondary Geometry Curriculum Sequencing?

I am currently student teaching, and the main class that I am focusing on is a secondary geometry class. I am currently following my classroom mentors curriculum sequence which looks something like: ...
4
votes
3answers
247 views

Explanation challenge: Why is a spiral ray-gun difficult to aim?

In an off-topic discussion, I tried to explain to a student why a "ray-gun" that (somehow!) shoots a ray that followed a spiral path would be much more difficult to aim at a particular target (point ...
6
votes
1answer
123 views

Intuitive explantion: What is a Finsler metric?

Neither of the two most evident sources, MathWorld: "Finsler Metric." Wikipedia: "Finsler Manifolds." seems to provide me with the high-level intuition that I could convey to students in ~10 minutes....
7
votes
3answers
422 views

Will presenting non-Euclidean geometries to students before Euclidean geometry give them a better intuition about shapes on the plane?

This question is related to Is Euclid dead? or Should Euclidean geometry be taught to high school students?, but I am not asking about whether Euclidean geometry should be taught at all, but whether ...
4
votes
0answers
156 views

Explaining the algebra behind a problem in computer geography

For work, I tend to have to explain quantitative ideas to people with only some informal computer science training. Yesterday, my friend wanted to draw a map on his computer and was concerned we ...
13
votes
4answers
734 views

Wiggins' question #12

There's an interesting read: Conceptual Understanding in Mathematics by Grant Wiggins. In that text the author proposes "a test for conceptual understanding" which should be given "to 10th, 11th, and ...
11
votes
8answers
751 views

Symmetry - practical usages

My girlfriend is studying to become a math teacher, and asked me what I have ever used symmetries for. I'm a web developer, and do some designing from time to time, so I answered that symmetry have ...
28
votes
10answers
4k views

Is Euclid dead? or Should Euclidean geometry be taught to high school students?

Apparently Euclid died about 2,300 years ago (actually 2,288 to be more precise), but the title of the question refers to the rallying cry of Dieudonné, "A bas Euclide! Mort aux triangles!" (...
8
votes
3answers
305 views

Adoption / penetration rates for dynamic geometry software in secondary school

Dynamic geometry software (DGS) has been around for decades; Geometer's Sketchpad (not the first, but probably the most well-known commercial product) has been around since 1986. Wikipedia lists more ...
11
votes
4answers
873 views

Reasons to teach Thales' theorem

In a classical course on Euclidean, compass-and-ruler geometry, Thales' theorem has always had a prominent place. However, as the Wikipedia article says, It is equivalent to the theorem about ...
19
votes
8answers
2k views

Are there disadvantages to teaching complex numbers as purely geometrical objects?

Complex numbers are, or at least were to me, generally introduced like this: There's no number whose square is negative. That's a shame! Well, whatever - we'll make one up! Set $i^2=-1$ and declare ...
10
votes
3answers
250 views

Appropriate education level for this geometry problem

What's the appropriate education level for the following concise but non-trivial geometry problem? Points $A$, $B$, $C$ are collinear; $\|AB\|=\|BD\|=\|CD\|=1$; $\|AC\|=\|AD\|$. What is the set ...
21
votes
10answers
4k views

Pi or Tau? How should the circle constant be taught?

Tau ($\tau = 2 \pi$) has more merits in its application, but pi is the established standard in industry and education. Is the trade-off of teach-ability of circle concepts worth the subsequent ...
12
votes
2answers
312 views

What prerequisites would college students need for a course based primarily on Euclid's elements?

I love Euclid's elements, and would like to base a course around them. Before I can pitch it to my supervisors, I need to know where it would fit in the curriculum. While it begins from elementary ...
13
votes
8answers
3k views

Visual Pythagorean demonstration

I know that there is a visual demonstration of $a^2+b^2=c^2$ using a smalĺ piece of paper, but there are also a lot of variations. Which visual or drawing demonstration of the Pythagorean theorem can ...