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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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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 ...
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2answers
220 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," ...
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3answers
302 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 ...
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1answer
918 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 ...
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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 ...
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1answer
166 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 ...
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174 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.
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4answers
155 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? ...
7
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3answers
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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 ...
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4answers
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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 ...
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2answers
126 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'...
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2answers
220 views

Experience using Khan Academy badges for basic math courses

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 ...
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1answer
179 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 ...
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3answers
586 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 ...
6
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3answers
197 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 $S \subset \mathbb{R}^3$&...
6
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4answers
175 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 ...
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3answers
224 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 ...
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4answers
773 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 ...
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2answers
188 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 ...
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1answer
120 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....
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4answers
323 views

Why do standard geometry textbooks not start with trigonometry?

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 ...
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5answers
273 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 ...
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2answers
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 ...
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2answers
129 views

At what educational stage are angles greater than 180 introduced?

Prompted by the question, "How to denote angle?," I am interested to learn when students consider and reason with angles $> 180^\circ$. For example, when do they reason with an angle of $270^\...
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1answer
219 views

Applications of notable points and lines of a triangle

I am currently starting to teach math to highschool kids who don't do well on their own, and I'm teaching a guy about notable points and lines of a triangle (incenter, centroid, circumcenter, ...
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2answers
138 views

How to teach mass center for young people

Could anyone recommend me some software that helps me teach about the centroid of an object? Something that was dynamic on the computer screen. Destined for 18 ...
5
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1answer
94 views

Suitable Curriculum for Algebra through Pre-Calc students in One Class

I run a high school outreach program at UCLA called DMAP: Diversifying Mathematics And Physics (webpage: http://dmap.pbworks.com), which focuses on exposing groups underrepresented in advanced maths ...
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1answer
77 views

Looking for a classic paper “Vinner and Hershkowitz”

I can't find this ZDM article: Vinner, S., & Hershkowitz, R. (1983). On concept formation in geometry. Zentralblatt für Didaktik der mathematik, 83(1), 20-25. Could you help me? I was ...
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0answers
75 views

the role of context in mathematical discussions of units and measurement in web design

Knowing that pedagogy for each age group is different, I will say right off the bat I am talking about working adults. I am noticing more and more, that despite people's phobias about math, they are ...
4
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4answers
163 views

How to explain how to get an end point of a segment from the other end point and it's midpoint?

I've had to try to explain the following problem: Let $PQ$ be a line segment, given $P(x_1, y_1)$ and the midpoint $M(x_2, y_2)$, find the coordinates of $Q$. I always draw a diagram and draw $\...
4
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3answers
699 views

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 ...
4
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7answers
931 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 ...
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4answers
304 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 ...
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5answers
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 ...
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3answers
166 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 ...
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2answers
3k 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 ...
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2answers
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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 ...
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2answers
209 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 ...
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0answers
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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 ...
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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. ...
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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 ...
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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 ...
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2answers
176 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 ...
3
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2answers
176 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 ...
3
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6answers
211 views

Multidisciplinary problem

I am looking for ideas for an activity for high school students, which involves plane geometry and another field, such as algebra, series, etc... For example, in junior high there is a nice activity ...
3
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3answers
996 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 "...
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1answer
150 views

Geogebra for Blind People

I work in the University with students in a situation of disability, specifically, teaching them math and related things. I have a few students that are very visually impaired; they work with JAWS or ...
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1answer
185 views

calculus without analytic geometry

How much of introductory calculus can be learned without using analytic geometry or for that matter any algebraic notations but simple euclidean geometry? Are there any resources(new ones not the old ...
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3answers
179 views

Which math class should I take as an exchange student in the USA (OH)? [closed]

I will go to an American High School (Ohio) this summer for a year and I will probably be a junior. I got a list of all classes, but there are really many classes to choose especially math classes. I ...
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1answer
240 views

Geometric Algebra Resources

Geometric Algebra brings together algebra, geometry, vectors, complex numbers, and linear algebra. It provides a single unification of all elementary math and serves as an excellent basis for physics, ...