All Questions
214
questions
2
votes
2
answers
78
views
maximising sum of distances from $(-2,0)$ and $(2,0)$ to the unit circle $x^2+y^2=1$
Consider any point $P$ on the unit circle centred at the origin $O(0,0)$ in $\mathbb R^2$. Let $A$ be $(-2,0)$ and $B$ be $(2,0)$ be two point on the $x$-axis and $D$ be the sum of the two distances $...
- 49
26
votes
3
answers
2k
views
Is it possible to turn this geometric demonstration of the area of a circle into a rigorous proof?
In this New York Times article, Steven Strogatz offers the following argument for why the area of a circle is $\pi r^2$. Suppose you divide the circle into an even number of pizza slices of equal arc ...
- 20.6k
3
votes
0
answers
181
views
Question about the second derivative of a circle
I am trying to find the second derivative of a general circle but I can't seem to get the right answer.
My working goes as follows:
$$
(x-a)^2+(y-b)^2=R^2
$$
$$
2(x-a)+2(y-b)*\frac{dy}{dx}=0
$$
$$
\...
- 417
1
vote
2
answers
118
views
Finding the derivative of a Quarter-circle [closed]
I am trying to solve this
.
I am confused on what the question is asking for. Which area do I need to solve for and what equation should I be using which leads me to an answer? Any help is appreciated....
- 23
2
votes
0
answers
66
views
The average minimum distance between all points in a quarter of a circle and two points.
There is a quarter circle $O$ of radius $1$ centered on $\left (0,0 \right)$. There is a point $M$ at $\left ( \frac{\sqrt{2}}{2},0 \right ).$
I want to calculate the average of the distances between ...
- 21
0
votes
2
answers
89
views
Calculus - Value of $\int\int _A xy dxdy$ between two circles using double integration (no polar coordinates)
This is my first post on this forum, so I'm sorry in advance if I come to the wrong section or something ...
I am currently stuck on an exercise of an exam given in my math college. The exercise is ...
- 1
4
votes
2
answers
302
views
Area of $(x-3)^2+(y+2)^2<25: (x,y) \in L_1 \cap L_2$
Two lines $(L_1,L_2)$ intersects the circle $(x-3)^2+(y+2)^2=25$ at the points $(P,Q)$ and $(R,S)$ respectively. The midpoint of the line segment $PQ$ has $x$-coordinate $-\dfrac{3}{5}$, and the ...
- 1,254
0
votes
1
answer
227
views
Is there any way to circumference of a circle with radius but without pi? [closed]
Please let me know if anybody knows how to calculate the circumference of a circle with radius but without pi?
0
votes
3
answers
518
views
The radius of a circle, having maximum area, which touches the curve $y = 4 – x^2$ and the lines, $y = |x|$ is
The radius of a circle, having maximum area, which touches the curve $y = 4 – x^2$ and the lines, $y = |x|$ is
Note this is different from: this which is asking for minimum area.
If you click on the ...
- 1,254
0
votes
1
answer
218
views
Countable vs uncountable infinitesimals in calculus
There is a general understanding that some infinities are bigger than others, in particular the infinity of the integers, the countable set of infinite discrete elements, and that larger infinity of ...
- 127
1
vote
1
answer
142
views
Finding the differential equation of a circle touching three curves $f(x,y)=0$, $g(x,y)=0$, $h(x,y)=0$
Find the differential equation of a circle tangent to three given curves:
$$ f(x,y)=0,\; g(x,y)=0,\; h(x,y)=0$$
Found a simple locus recently using analytical geometry.
Circle Touching 2 lines & ...
- 41k
0
votes
0
answers
181
views
Equation for a heart
I’m trying to determine the equation for a heart starting from the unit circle. I figured a way to do it is to go from progressively closer shapes. What is the equation for shapes A-D? The very first ...
- 27
0
votes
2
answers
263
views
Coordinates on 3d Circle
Problem:
Given is is the centerpoint $C$ of a circle and two extra reference points $R$ and $E$, which are laying on the circle.
While as the line $\overline{CE}$ is defining the zero point on the ...
- 103
1
vote
1
answer
140
views
Area of a region bounded by a circle and vertical line using integration
What is the area of the right region bounded by $x^2 + y^2 =25$ and $x = -3$?
My attempt solution: I solved first for the area of the left region and subtracted it from the area of the circle, which ...
- 73
0
votes
2
answers
609
views
Area of a Region Bounded by a Circle and Vertical Line
What is the area of the right region bounded by $x^2 + y^2 =25$ and $x = -3$?
My attempt solution: I solved first for the area of the left region and subtracted it from the area of the circle, which ...
- 73