Mixing
Space encompassing all possible secant segment endpoints
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I’m going to preface this by stating that i have no knowledge of this type of math and so my word choice will most likely not meet established standards. I’ll do my best to correct myself as we go here.
I have a space defined by the intersection of two circles of equal radius with the distance between them equaling that same radius and a line that goes through both circles center. It ends up looking like an equilateral triangle with two curved sides. For this space I need to define a second search space which encompasses at least one endpoint to all possible secant lines through the space that are one circle’s radius in length or less. In addition no secant endpoint may lie below the center-to-center line.
I’m just looking for an optimal space that is both small and geometrically simple. Just a direction that i could go for research or something would be wonderful, I’m having difficulty finding resources on this type of subject.
Thank you so much
geometry secant
asked Jul 27 at 17:38
Charles Vail
164
add a comment |Â
up vote
1
down vote
favorite
I’m going to preface this by stating that i have no knowledge of this type of math and so my word choice will most likely not meet established standards. I’ll do my best to correct myself as we go here.
I have a space defined by the intersection of two circles of equal radius with the distance between them equaling that same radius and a line that goes through both circles center. It ends up looking like an equilateral triangle with two curved sides. For this space I need to define a second search space which encompasses at least one endpoint to all possible secant lines through the space that are one circle’s radius in length or less. In addition no secant endpoint may lie below the center-to-center line.
I’m just looking for an optimal space that is both small and geometrically simple. Just a direction that i could go for research or something would be wonderful, I’m having difficulty finding resources on this type of subject.
Thank you so much
geometry secant
asked Jul 27 at 17:38
Charles Vail
164
It is not at all clear what you are looking for. What do you mean by "search space"? Is it not the case that any point on the curve is an end-point of a secant that is no longer than the radius? And how can a secant endpoint be below the centre-to-centre line (and hence outside the curve)? (We usually talk about secants of "curves" not "spaces".)
– Rob Arthan
Jul 29 at 16:42
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I’m going to preface this by stating that i have no knowledge of this type of math and so my word choice will most likely not meet established standards. I’ll do my best to correct myself as we go here.
I have a space defined by the intersection of two circles of equal radius with the distance between them equaling that same radius and a line that goes through both circles center. It ends up looking like an equilateral triangle with two curved sides. For this space I need to define a second search space which encompasses at least one endpoint to all possible secant lines through the space that are one circle’s radius in length or less. In addition no secant endpoint may lie below the center-to-center line.
I’m just looking for an optimal space that is both small and geometrically simple. Just a direction that i could go for research or something would be wonderful, I’m having difficulty finding resources on this type of subject.
Thank you so much
geometry secant
asked Jul 27 at 17:38
Charles Vail
164
I’m going to preface this by stating that i have no knowledge of this type of math and so my word choice will most likely not meet established standards. I’ll do my best to correct myself as we go here.
I have a space defined by the intersection of two circles of equal radius with the distance between them equaling that same radius and a line that goes through both circles center. It ends up looking like an equilateral triangle with two curved sides. For this space I need to define a second search space which encompasses at least one endpoint to all possible secant lines through the space that are one circle’s radius in length or less. In addition no secant endpoint may lie below the center-to-center line.
I’m just looking for an optimal space that is both small and geometrically simple. Just a direction that i could go for research or something would be wonderful, I’m having difficulty finding resources on this type of subject.
Thank you so much
geometry secant
asked Jul 27 at 17:38
Charles Vail
164
asked Jul 27 at 17:38
Charles Vail
164
asked Jul 27 at 17:38
Charles Vail
164
asked Jul 27 at 17:38
Charles Vail
164
164
It is not at all clear what you are looking for. What do you mean by "search space"? Is it not the case that any point on the curve is an end-point of a secant that is no longer than the radius? And how can a secant endpoint be below the centre-to-centre line (and hence outside the curve)? (We usually talk about secants of "curves" not "spaces".)
– Rob Arthan
Jul 29 at 16:42
add a comment |Â
It is not at all clear what you are looking for. What do you mean by "search space"? Is it not the case that any point on the curve is an end-point of a secant that is no longer than the radius? And how can a secant endpoint be below the centre-to-centre line (and hence outside the curve)? (We usually talk about secants of "curves" not "spaces".)
– Rob Arthan
Jul 29 at 16:42
It is not at all clear what you are looking for. What do you mean by "search space"? Is it not the case that any point on the curve is an end-point of a secant that is no longer than the radius? And how can a secant endpoint be below the centre-to-centre line (and hence outside the curve)? (We usually talk about secants of "curves" not "spaces".)
– Rob Arthan
Jul 29 at 16:42
It is not at all clear what you are looking for. What do you mean by "search space"? Is it not the case that any point on the curve is an end-point of a secant that is no longer than the radius? And how can a secant endpoint be below the centre-to-centre line (and hence outside the curve)? (We usually talk about secants of "curves" not "spaces".)
– Rob Arthan
Jul 29 at 16:42
add a comment |Â
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It is not at all clear what you are looking for. What do you mean by "search space"? Is it not the case that any point on the curve is an end-point of a secant that is no longer than the radius? And how can a secant endpoint be below the centre-to-centre line (and hence outside the curve)? (We usually talk about secants of "curves" not "spaces".)
– Rob Arthan
Jul 29 at 16:42