Tagged Questions
0
votes
2answers
38 views
What is the initial reason to define the evolute of a curve?
The evolute of a curve is defined as the envelope of the normals or as the locus of the center of the osculating circle.
What is exactly "the envelope of the normals" ?
What is the reason to ...
2
votes
1answer
107 views
How do we know $\pi$ is a constant? [duplicate]
How did the ancient Greeks discover that the ratio of a circle's circumference to its diameter is constant? It does not seem so intuitive. Thanks!
4
votes
3answers
139 views
History of Conic Sections
Recently, I came to know that ancient Greeks had already studied conic sections. I find myself wondering if they knew about things like directrix or eccentricity. (I mean familiar with these concepts ...
1
vote
0answers
63 views
How was the isoperimetric inequality formulated?
I'm tyring to understand how the isoperimetric inequality came into existence.
It seems like finding the region which yields maximum area when enclosed by a curve of fixed length
is an old problem. ...
2
votes
0answers
129 views
On the geometric arguments used in Newton's *Principia Mathematica Naturalis Philosophae*
When one reads Newton's Principia Mathematica, one is immediately aware of the complexity of the synthetic geometry that he uses to prove his propositions. This I understand because all of the ...
9
votes
1answer
376 views
ancient concepts and modern concepts
Is there an extant published expository account, comprehensible to all mathematicians, of the conceptual differences between ancient Greek mathematical concepts and modern ones?
I have in mind things ...
32
votes
4answers
1k views
Why is a full turn of the circle 360°? Why not any other number?
I was just wondering why we have 90° degrees for a perpendicular angle. Why not 100° or any other number?
What is the significance of 90° for the perpendicular or 360° for a circle?
I didn't ever ...
4
votes
2answers
253 views
the definition of the area of a surface
When we say the area of a rectangle is the product of the length by the width is it a definition based on geometric intuition or is it a result? I know it is a result that we can find after defining ...
7
votes
3answers
498 views
Volumes of cones, spheres, and cylinders
Given a sphere with radius r, a cone with radius r and height 2r, and a cylinder with radius r and height 2r, the sum of the volume of the cone and sphere is equal to the volume of the cylinder. If we ...
7
votes
1answer
259 views
who first defined a tangent to a circle as a line meeting it only once?
From googling, it seems commonly believed that Euclid did this, but it seems nowhere in Euclid does he even state this property of a tangent line explicitly. Rather Euclid gives 4 other equivalent ...
