Questions tagged [geometry]
For questions related to geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.
139
questions
2
votes
0answers
51 views
Logic and proofs in secondary school
Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...
10
votes
11answers
4k views
Ideas for explaining 4D and higher dimensions
I introduced the hypercube (to undergraduate students in the U.S.) in the
context of generalizations of the Platonic solids, explained its
structure, showed it rotating.
I mentioned Alicia Stott, who ...
1
vote
1answer
115 views
Workbooks for advanced high school math topics
I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them):
Logic and sets (propositional calculus, ...
36
votes
12answers
4k views
Beautiful planar geometry theorems not encountered in high school
I would like to impress college students (undergraduates in the U.S.)
that there is more to planar geometry beyond what they learned in high school. I would like to show them beautiful theorems they ...
14
votes
4answers
377 views
When Euclid was used as a textbook, what exercises did students do?
Until fairly recently, it was common for students in school to learn Euclidean geometry from a translation of Euclid. I get the impression that ca. 1700 this would have been in college and only for a ...
19
votes
2answers
709 views
Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?
When I taught courses on algebra giving a first exposition to Galois theory I usually included some discussion of classical results showing the impossibility of constructing certain points with ruler ...
3
votes
1answer
644 views
Which book should I refer to for analytical solid geometry?
I am an undergraduate student and since this is a site of math educators, I thought of putting this question (more accurately a query) here. Can you list some good books on analytical solid geometry?
42
votes
37answers
17k 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 ...
34
votes
17answers
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
...
3
votes
2answers
139 views
Should we stop using traditional compass in schools & start/encourage adopting compasses like “Slide N Measure” or “Safe-T” compasses instead?
I think using the traditional compass with those styluses that can literally be used to hurt or accidentally hurt someone are very dangerous. Most people don't use these in day-to-day life anyways, ...
11
votes
4answers
980 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 ...
12
votes
2answers
153 views
2D drawings of 3D objects in printed school textbooks: orthogonal or perspective?
There is a tradition in the use of orthogonal projections to represent 3D objects in printed school math textbooks. On the other hand, perspective projections represent better the way as we "see" real ...
6
votes
5answers
2k views
What are strategies for teaching that the altitude of a right triangle creates two similar triangles?
If you draw the altitude to the right triangle as shown, it is easily seen that $$\triangle KLM\sim\triangle KNL\sim\triangle LNM.$$ This in turn leads to several interesting proportional relations ...
2
votes
3answers
154 views
Mnemonic for volume of cone $V=\frac{1}{3}\pi r^2 h$ [closed]
Does anyone have a good mnemonic for the volume of cone formula: $$V=\frac{1}{3}\pi r^2 h?$$
3
votes
2answers
166 views
Introducing quadric surfaces in high school
I am presenting an enrichment session on 3D geometry and quadric surfaces to able 15-year-old secondary school students. They know algebra but not calculus. They have learned about equations of ...
4
votes
2answers
408 views
Euclid Book 1 Proposition 4 [closed]
In Euclid's The Elements, Book 1, Proposition 4, he makes the assumption that one can create an angle between two lines and then construct the same angle from two different lines. I do not see ...
8
votes
3answers
687 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 ...
-1
votes
1answer
214 views
Integrated math curriculum in different countries
One of the selling points of re-hashed American 1990s high school math programs is that they are "integrated", that is, combine algebra, geometry, statistics, trigonometry just like the European ...
1
vote
1answer
95 views
How to teach geometric patterns? [closed]
I would like to know how to teach geometric patterns in secondary school. I want to elaborate worksheets, which could include different kinds of strategies related to this topic.
Are there resources ...
3
votes
0answers
145 views
Cinderella vs. GeoGebra
I would be grateful for a comparison between
the capabilities of Cinderella and
Geogebra, for teaching
at all levels, but especially at the college/university-level.
I became a reasonably adept user ...
4
votes
1answer
189 views
How to explain angle hunting to students
$I$ is a point of the circle of diameter $JK$. The perpendicular bisector of $JK$ cut the semi-circle not containing $I$ at $M$. Let $N$ and $P$ be the orthogonal projections of $M$ on $IJ$ and $IP$. ...
10
votes
4answers
1k views
Co-curricular lessons between geometry and chemistry?
My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. I'm on ...
-1
votes
4answers
276 views
Good textbooks for a college Basic Geometry course?
I will be teaching geometry for the first time ever this summer. I teach at a community college, and we only offer this course in the summer. (Mostly high school students take it, but it is a college ...
28
votes
12answers
7k views
How to give my students a straightedge instead of a ruler
I'm having a "challenge" in my geometry classes getting students to avoid using rulers as measuring devices in constructions. As natural as that usage is, they're only supposed to use them to connect ...
2
votes
1answer
130 views
Recommend a website for creating geometric figures
For teaching geometry, it could be useful to have a website where one can enter the names of vertices of a polygon, specify which diagonals should be depicted, and specify the measures of certain ...
2
votes
2answers
356 views
High school maths textbook for talented students
I am looking for a math textbook. I'm 15 and I'd like to complete
algebra 2 geometry and perhaps something about probability/ number theory or trigonometry would be nice too. Later I wanna do ...
8
votes
1answer
570 views
An alternative to “two column” geometry proofs
I'm a high school teacher in New York State (US), starting in on my first year of teaching Geometry. One of the things that really intrigues me is that the Regents exam (the state-mandated final exam)...
4
votes
4answers
549 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 ...
4
votes
3answers
260 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 ...
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 smalÄŗ piece of paper, but there are also a lot of variations.
Which visual or drawing demonstration of the Pythagorean theorem can ...
4
votes
3answers
248 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 ...
16
votes
5answers
1k views
Should my 8th graders see a proof of the Pythagorean Theorem?
I've been teaching the Pythagorean Theorem in my 8th grade class, and I noticed something odd. In the book I'm using, the sequence goes something like this:
Motivate the idea of distances on a grid
...
10
votes
0answers
327 views
Use of Lockhart's *Measurement* in a course?
I greatly admire Paul Lockhart's
Measurement
(Harvard Press).
Many of you know him through
A Mathematician's Lament.
One review of Measurement said,
āHere Lockhart offers the positive side of the ...
11
votes
1answer
378 views
Using number theory instead geometry to introduce proof in Basic School?
It seems there is an overall agreement that Geometry is the right place to introduce proof in Basic School. However, number theory (arithmetic) looks like to be a more simple environment (consider, ...
5
votes
4answers
359 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 couldnāt help but wonder where ...
7
votes
3answers
239 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 $S \subset \mathbb{R}^3$&...
4
votes
1answer
219 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 ...
1
vote
0answers
114 views
Missouri EOC and the best Geometry book
I am a Missouri High School Geometry teacher. WE are adopting textbooks this year. I would like opinions on which books are most closely aligned with the Missouri Learning Standards because at the ...
6
votes
4answers
196 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 ...
16
votes
3answers
465 views
Good lessons/activities for one-day subs
In my school district, and I'm sure most others, every teacher needs to have a set of "emergency lesson plans", in case they are sick or need to be out for a day, so that the substitute can have ...
2
votes
2answers
106 views
Are questions on overlapping solids of revolutions without prior definitions and instructions fair given that there are divided interpretations?
If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the ...
9
votes
6answers
370 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 ...
26
votes
17answers
14k views
Given a 3 4 5 triangle, how do you know that it is a right triangle?
Without knowing the Pythagorean theorem, and in presenting reasons why the theorem might be true (without giving a full proof), is there any way to give examples of triangles that are intuitively ...
2
votes
3answers
151 views
How to give a good Geometry test? [closed]
Generally, in a Geometry test, you'd need to test proofs (Prove that triangle XYZ and ABC are congruent).
On the other hand, proofs depends depends on theorems which depend on postulates, which are ...
7
votes
4answers
280 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
votes
1answer
204 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 ...
28
votes
11answers
23k views
Why should kids learn how to use a compass and straightedge, and not rely on a drawing program?
I am curious why it is necessary for people to learn how to use compasses and straightedges in geometry, and not just rely on a drawing program.
I have a couple ideas, but I might be missing ...
2
votes
0answers
52 views
Geometry sample tests
I am teaching intro to Geometry using Moise and Downs textbook. It is an excellent text but somewhat old.
Does anyone know if there are sample tests that are available for use with this textbook?
19
votes
12answers
9k 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.
4
votes
0answers
153 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 ...
