# 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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### How to justify formula for area of triangle (or parallelogram)

I'm going to be teaching my kids the concept of area soon. The concept of area of a rectangle (or square), $\text{base} \times \text{height}$ is fairly easy to both explain and intuit: you can break ...
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### Math textbook for secondary school using Logo like language

What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
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1 vote
105 views

### Math textbook for secondary school using Logo like syntax

What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
• 83
139 views

### When can students understand the intersection of two circles?

I'm interested in learning two transitions: (1) When can students reason (intuitively, but accurately) to conclude that two circles in the plane could intersect in $0$, $1$, or $2$ points, or are ...
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### Comparison of two ways to introduce translation to 12-14 year olds

I consider pupils 12-14 years old, who are new to translation. On the other hand, they have been accustomed to placing points in a coordinate system, especially when studying relative numbers. In ...
230 views

### About a difficult exercise for 12 years pupils

You have to go from a point $A$ (start) to a point $B$ (arrival) by crossing a river $(d)$ and traveling as little distance as possible. Pupils first do a search by trying several paths $1,2,3,4$ and ...
191 views

### Infinite descent method in geometry

What are the examples we can use to explain infinite descent as an efficient method of proofs in geometry? I think one of the best may be proving medians of a triangle are concurrent by the infinite ...
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### Textbook For a Course on Classical Geometry

I have been assigned to teach a first year course in geometry the next academic year. This course has been running for quite a while in the university, but of late, has been thought of as redundant ...
1 vote
190 views

### Proof that volume of cone is 1/3 that of a cylinder [closed]

I am trying to verfy the formula for "cone volume" calculation. It is not clear why cone volume is 1/3 of a cylinder volume with the same bottom size and height. Is there any proof of the ...
4k views

### What are some common errors and misconceptions about the Pythagorean Theorem?

I'm teaching a geometry class and want to ensure my students understand the most common errors and misconceptions related to the Pythagorean Theorem and its applications. I attempted an initial Google ...
1 vote
395 views

### Is there a particular reason why segment addition postulate and partition postulate are two different things?

I could be wrong but those two ideas sound the same, just that the partition postulate is more general. There is also the angle addition postulate. The segment addition postulate states that if three ...
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### Geometrical verifications for Algebraic formulae

What is the importance of using approaches related to Geometric Algebra in teaching,is it only useful when introducing Algebra to the students or can it be helpful to improve creative skills in ...
• 1,144
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### What benefit is there to obfuscate the geometry with algebra?

Consider: In a right triangle: sin(2x + 4) = cos (46) What is the value of x? The question above is from standardized tests for a geometry course. If my goal is to have students understand ...
• 1,068
1 vote
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### Is it correct to state that a cone has no faces?

Faces are attributes of polyhedra, so it doesn't make sense to ask how many faces a cone has. Are there traditional scholars that use faces attached to cones? How do different countries deal with the ...
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### How to properly define volume for beginner calculus students?

I'm interested in opinions based on experience about how to introduce volume for beginner calculus students. Below I present some observations and specific questions. In Stewart's book, the volume of ...
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### Geometric line: constructing fractions

I am interested in teaching maths visually. in page 36 of Growing ideas of number (by John N Crossley) the following image appears, yet I cannot fully grasp how to interpreted it.
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### How to convince a student without calculus that great circles are geodesics in a sphere?

how to convince or demonstrate to a high school student who does not know differential and integral calculus that the geodesics of a sphere are arcs of great circles?
432 views

### How to explain square meters?

How can we explain to students these ideas? A square with 4 sides measuring 25 cm each does not have an area of 1 square meter. A shape which is not a square can have an area of 1 square meter. Is “...
2k views

### Models for spherical geometry

Context: I am an associate professor at a small liberal arts institution in the US. I am currently preparing to teach geometry this fall. Our course is mostly focused on Euclidean geometry (it's ...
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1 vote
665 views

### Triples or triplets in Pythagoras theorem

We usually say (3,4,5) , (5,12,13) as Pythagorean triples. What is much better way to refer those sets of numbers, Pythagorean triples or Pythagorean triplets? According to the normal usage we say ...
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### Multiple proofs for the same problem

One way of encouraging students to explore mathematics can be letting them to use different approaches to solve the same problem. If students can find alternatives from different areas of mathematics ...
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### Geometrical approaches in algebra

Usually we describe proofs in algebra by algebraic means, I think it may be useful to introduce geometrical approaches to those proofs to improve creativity skills of students, what are the examples ...
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389 views

### Best demonstration of $\pi$ ever; is this common?

When I was in 6th grade (U.S. so 12-13 years old), I took a summer school class. The teacher gave us all different sized spools (spools that hold sewing thread but were empty). We each made a mark on ...
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### How to formalize high-school (Euclidean) geometry?

I have unsuccessfully attempted several times over the years to formalize high-school (Euclidean) geometry, or even a working subset of it. Think very simple, diagramless geometry. The usual two-...
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### Geometry in the Community College Curriculum

As many Americans know, the “traditional” high school sequence is: Algebra 1 Geometry Algebra 2 PreCalculus Calculus For those who take developmental education at the community college level, it ...
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### Matriculation exams like in Europe

I just looked at matriculation exams from Finland. They have both basic and advanced level exams. Most US high school seniors could not pass the basic exam. If each US state were to create its own ...
1k views

### What is a good second book in high school geometry?

I have been looking at questions on Math Stack Exchange and I am frequently coming across topics that sound as if they could have been optional chapters in a high school geometry class, but I have ...
3k views

### Should figures be presented to scale?

I've been working with a teacher, helping her with tech. One of the things I help with is to convert PDF formatted quizzes or tests to DeltaMath for the students to take online. The issue that I face ...