# 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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279 views

### Learning Math like Euclid

I'm posting this here as it's off-topic for the Math stack exchange, and I'm hoping there will be some educators here that can point me in the right direction. I enjoyed watching the YouTube series ...
199 views

### Coverage of Fundamentals of Lines and Planes

I was helping a high school student with some fundamental concepts of planes and lines, when I realized I am rusty on some definitions myself. I found some minimal coverage in his high school math and ...
262 views

### Book recommendations on mathematics education focusing on geometry

I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education). Is there some recent (as concise as ...
237 views

### Resource to supplement to Euclid's Elements

I am an instructor at a mid-sized American university, preparing to teach a two-quarter geometry course for junior and senior math majors. My plan is to use Hartshorne's "Geometry: Euclid and Beyond," ...
303 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 ...
1k views

### What is the term for the marks used to show congruence in geometric figures?

When looking at a given picture to be used in a geometric proof, often times single, double, or triple "slashes" mark off equal line segments or arcs. What is the correct term for these? I've seen ...
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 ...
170 views

### The role of “area” in a Common-Core aligned high school classroom

Some background: I recall becoming much more adept at the concepts of area and measurement during high school geometry. However, as I scour the Common Core standards, "area" only shows up in high ...
177 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.
164 views

### Making physical 3D models

I was thinking to make classroom illustrations of some 3D mathematical objects, such as graphs of 2 variable functions, minimal surfaces, etc. My question is, what would be a good way to go about it? ...
403 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 ...
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 ...
145 views

### Drawing vs Constructing

How would you explain to students the difference between drawing and constructing? "Accuracy" seems to be a go to word, but that's not really what the difference is. I want to say more, but I also don'...
221 views

This semester I am teaching a basic geometry course for design students (interior and industrial), which I am making strongly project-based since I believe they need to learn how to use geometry "in ...
186 views

### Fun classroom exercise for mental rotation

I'm training to be a teacher and I am doing a maths lesson later next week. The topic is geometry, the students are 12-year-olds. More concretely, I've been given a selection of exercises that I may ...
596 views

### In what curricula are “rectangles” defined so as to exclude squares?

Most contemporary curricula define the word "rectangle" inclusively, so that all squares are automatically rectangles. Are there curricula in which this convention is not followed? That is, are ...
216 views

### Why is it difficult to freely change between points and vectors?

I have noticed working with bright undergraduates that it is not uncommon for them to have difficulty easily converting between a point—say, a point $p$ on a surface $S \subset \mathbb{R}^3$&...
176 views

### Group theory by geometry

I'm introducing my kids to the concepts of group theory. To make abstract things tangible, I'm trying the geometry way, adopting Arnold's in "Abel's Theorem", so far I've explained, by using symmetry ...
246 views

### Wording VS mathematical notations

Is it better to write everything in words as the concepts themselves should be known? Or will some teachers in some countries prefer to be able to choose questions which also test the student's ...
815 views

### Integrate Coding into the Geometry Curriculum

My supervisors want to see coding integrated into the ninth grade Geometry class. This class is mostly concerned with proofs--not too much algebra. These students know a decent amount of the visually ...
193 views

### How to reasonably denote lines, line segments and rays?

I'm teaching geometry at high school for the first time soon and am struggling to find a reasonable notation for lines, line segments and rays defined by two points $A$, $B$ (and a direction). At the ...
122 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....
336 views

Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
277 views

### Should the construction of triangles be taught?

Constructing triangles (or other shapes) seems to be quite an obsolete topic, and yet, they feature in almost every high school math competition, to disappear completely in college. In recent years in ...
138 views

### Approaches to Teaching for Questions Around Partitioning Space

My students are preparing for their SATs and have problems with a certain type of questions, i.e., questions involving a geometrical figure and $n$ (usually $n = 2,3$) straight lines passing through ...
135 views

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### A formula for the area of a rectangle [closed]

This is a question about elementary geometry, so I think it belongs on this site. Let $d$ be the length of a diagonal in a rectangle, and let $m$ be half the perimeter. Then a formula for the area ...
933 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 ...
338 views

### Teaching congruent triangles non-rigorously

I've just started teaching congruent triangles to a class of 14/15 year olds in the UK. All that they are required to know for the purpose of national exams here is that two triangles are congruent if ...
115 views

### Books and worksheets on symmetry

At a local Math Circle, I loved some problems worked out through a hinged mirror to illustrate symmetry. I bought a hinged mirror from hand2mind.com, and am looking for some material, ideally books ...
245 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 ...
223 views

### Geometry textbook with an abstract algebra emphasis

I'm teaching a variety of undergraduate and graduate geometry classes (mostly for in-service teachers) which range from elementary axiomatic geometry to more advanced transformational geometry. I'm ...
171 views

### Resources for precalculus applications

Do you know any good sources of free/open application-style problems for the precalculus level? I would like to use an OER precalculus book, but the few I am most happy with seem to lack (what we ...
4k views

### Notation of line segment and its length

I have sometimes seen a notation where $AB$ could mean either the line segment or its length. Why do the same notation can be mean both? Should one teach pupils to use for example notation $d(A,B)$ or ...
135 views

### How are geometric proofs related to geometric pictures?

When teaching geometry it is common to use pictures/figures to "show" the problem and its solution. It's also common to say things like "more than one figure can be shown which demonstrates the same ...
147 views

### Intuition: 5 regular polyhedra, 6 regular 4-polytopes, and then 3 regular d-polytopes

I have struggled to offer an intuitive explanation (to U.S. college students) why the number of regular polytopes in dimension $d$ is: $d=2$, number: $\infty$. $d=3$, number: $5$, the five Platonic ...
96 views

### Why define the names of quadrilaterals so that some categories (rhombus and rectangle) intersect and some (kite and trapezoid) are disjoint?

We're using Pearson's Geometry in my class. As terms are defined there, Parallelograms include Rhombi (congruent sides), Rectangles (right angles), Squares (congruent sides and right angles, i.e. ...
72 views

### What are the best expository pieces related to the Van Hiele models?

The Van Hiele model (wikipage) "is a theory that describes how students learn geometry." I would appreciate further insights into the original model, later models that expanded or re-worked it, and ...
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 ...
533 views

### Rhombuses, kites etc

As a high school teacher, I sometimes wonder about the usefulness of certain topics. Some topics seem to be in the textbook because they have always been there, not because they lead anywhere ...
194 views

### Is the Nomenclature of Triangle Congruency Proofs Consistent?

My Geometry class is doing triangle congruency proofs these days. In general, we find three pairs of congruent parts (sides or angles) in two triangles; we show that these congruencies reveal that the ...
177 views

### “A” or “The” Cartesian plane?

Which is correct terminology: "A Cartesian plane" or "The Cartesian plane"? (As in the directions for a section of homework being, "Plot a point on ______ Cartesian plane." In that context, I feel ...