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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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 “...
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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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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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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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How can I build a protractor without a protractor?
We all know how to use a protractor; it is taught in elementary school. However, I was wondering what type of knowledge is required to build one from scratch.
For instance, was the understanding of $\...
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Is "Annular Ring" redundant?
I've come across the term annular ring in parentheses following washer in my calculus textbook: "has the shape of a washer (an annular ring)". The definition of the word "annular" ...
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Explaining why volume of cone is a third of cylinder
I came across this video explaining to kids why the volume of a cone is a third of the cylinder of same cross-sectional radius and height. Essentially the explainer presents pre-created cylindrical ...
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Real-world applications of taxicab metric
The taxicab metric can be used to measure distances in idealized gridded cities. However, usually this serves only as a fun exercise for students.
I'm looking for engaging (as non-technical as ...
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Resources for Teaching Parameterization of Curves/Surfaces
In classes like Calc 3 or Computer Graphics, I want my students to be comfortable describing common curves and surfaces parametrically (such as lines, triangles, circles, or surfaces of revolution). ...
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Creative problems in 2D vector geometry
What are some "interesting" and creative problems or exercises on specifically 2-dimensional vector geometry that a high school student might find compelling to solve?
The class' current ...
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Why do so many children's book confuse discs with circles? [duplicate]
The difference between a disc (disk) and a circle is crystal clear to me:
However, in many children's books, a disc is usually called a circle:
Why do many children's book confuse discs with circles?...
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Is there a good Animation to explain Rotational Symmetry of Equilateral triangle
I am willing to teach that the Order of rotational Symmetry of Equilateral triangle as $3$ using Animation. Any suggestions of good applet which demonstrates the rotation of equilateral triangle with ...
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Valid Reasons in Two-Column Geometry Proofs
I'm wondering about the relationship between Eculid's work and modern high school geometry. In "two column proofs," certain reasons are considered acceptible for steps in the proof, such as ...
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How do I sketch a good gaussian curve freehanded, or by using only common sketching tools?
I'm a lousy artist. If I want my Gaussian curves to be accurately drawn when I use a whiteboard, or work with pen & paper, what are my options?
Is there a way to use a straight edge, or compass, ...
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Line segments on a geoboard
To make a polygon on a traditional geoboard, one usually stretches a rubber band around the vertices. No problem there.
When making a simple line segment, however, a rubber band is typically stretched ...
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Where can I buy a compass that can hold an "Expo" dry erase whiteboard marker?
Question in title. I'd like to draw a perfect circle on the whiteboard using "expo" dry erase markers. Is there a store I could buy such a compass at? Thank you
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Names of two circle theorems in English [closed]
There are two theorems:
All three angles AC_1B, AC_2B, AC_3B are equal. In general: All angles above a chord are equal.
The size of any angle above a chord AB is half the size of angle AOB where O is ...
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Explain to 10 year old — Why do 3D mental pictures usually suffice for high-dimensional geometry?
My 10 year old daughter is trying to read this book — please explain in Simple English that she'll grasp. Kindly see the embolded phrases below. The author doesn't expound why the 3D "mental ...
user155
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Is it a good idea for elementary school students to observe and discover the "circle perimeter formula" themselves without being dictated to?
Let them discover $\;\ell=2\pi R\;$ by their own, at least the invariance of $\ell/R$
Do you think that the following method works well in a mathematics class of elementary school? What do you think ...
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Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?
The assumed age of the students is 10-15 years old.
What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
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What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?
The imagined students are in elementary school, say around 9-13 years old.
I want to use rather precise terminology when talking to my students. However, it seems like we typically use the same ...
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Are there any list of mathematical constructions which can challenge 12-16 year old students?
Mathematical (geometric) constructions are an interesting way to engage students. It also helps in better understanding of different geometrical properties.
For example, Sierpinski triangle or square, ...
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Geometric and Graphical perspective on completing the square
I just read an interesting article that helps to understand completing the square, and prove the quadratic equation from a geomterical perspective.
My question is how do I understand the graphical ...
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What is the preferred way to denote the Pythagorean theorem equation?
I am teaching 12-16 year olds.
How should I write down the Pythagorean theorem equation?
Some alternatives:
$a^2 + b^2 = c^2$
$\text{leg}^2 + \text{leg}^2 = \text{hypotenuse}^2$
$\text{leg}_1^2 + \...
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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 ...
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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 ...
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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 ...
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Can we define length and perpendicularity not via an inner product?
A natural way to reason about Euclidean geometry
using modern mathematical language
is to define Euclidean space
as an affine space $A$
directed by a finite-dimensional real vector space $V$.
However, ...
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Is $\overline{AB} \cong \overline{BA}$ usually taught as an instance of the symmetric property of congruence?
I have been tutoring a wide range of math subjects for many years. Recently, I began tutoring a girl in high school geometry (in California, for context). This semester of the course is starting with ...
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Definition of Trapezoid
From one textbook we use in our High School -
Transcription:
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid.
And from ...
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How to teach the Pythagorean theorem in a satisfying way to high school students?
I've been pretty dissatisfied with the way the Pythagorean theorem is usually taught, mainly for two reasons:
The chosen proof feels like magic and I don't feel like I have a better understanding of ...
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US High School Geometry: What are all the "reasons" allowed in two column proofs?
For a project I am considering on geometry in US high schools, I need a list of all the reasons that are usually allowed in two column geometry proofs there. I have a bachelor's degree in math and ...
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What is an algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? [duplicate]
Q: What is a succinct, clear and purely algebraic explanation of why
the product of the slopes of perpendicular lines is $-1$?
Here I am aiming for high-school students (in the U.S.).
I have a purely ...
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Is there a name for paths that follow gridlines?
I'm writing up an activity where students are looking at pathlengths that follow along gridlines.
Is there a word or phrase that is commonly used to describe those paths, but doesn't include ...
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Is there online geometric construction software that models physical constructions?
In this weird pandemic school year, I'm doubly interested in technology integration to help my virtual (high school) students as much as my in-person students. I've been particularly eager to get ...
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Which Geometry book is more rigorous/harder?
Can anyone please tell me if the AOPS (Art of Problem Solving) Geometry is more rigorous/difficult generally than a book called "Geometry for Enjoyment and Challenge" by authors Rhoad, ...
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College undergraduate geometry courses
I am interested in learning how a course in geometry is employed today
at undergraduate colleges/universities in the U.S.
On the one hand, such a course seems to serve as an optional (rarely required)
...
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