Stadium Seating - Geometric Sequences
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A circular stadium consists of sections as illustrated, with aisles in between. The diagram show the tiers of concrete steps for the final section, Section K. Seats are to be place along every step, with each seat being 0.45cm wide. AB, the arc at the front of the first row is 14.4m long, while CD, the arc at the back of the back row is 20.25m long.
$hspace{2in}$ 
1) How wide is each concrete step?
2) What is the length of the arc of the back of Row 1, Row 2, Row 3, etc.?
3) How many seats are there in Row 1, Row 2, Row 3, ……, Row 13?
4) How many sections are there in the stadium?
5) What is the total seating capacity of the stadium?
6) What is the radius of the ‘playing surface'?
sequences-and-series geometry
edited Jul 29 '15 at 12:37
David K
51.8k340114
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
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show 1 more comment
up vote
1
down vote
favorite
A circular stadium consists of sections as illustrated, with aisles in between. The diagram show the tiers of concrete steps for the final section, Section K. Seats are to be place along every step, with each seat being 0.45cm wide. AB, the arc at the front of the first row is 14.4m long, while CD, the arc at the back of the back row is 20.25m long.
$hspace{2in}$
1) How wide is each concrete step?
2) What is the length of the arc of the back of Row 1, Row 2, Row 3, etc.?
3) How many seats are there in Row 1, Row 2, Row 3, ……, Row 13?
4) How many sections are there in the stadium?
5) What is the total seating capacity of the stadium?
6) What is the radius of the ‘playing surface'?
sequences-and-series geometry
edited Jul 29 '15 at 12:37
David K
51.8k340114
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
Welcome to Math.SE! Please review How to Ask for ways to improve your Question. As it currently reads, you have multiple parts with no indication of where you may be having difficulty, and there's no context to motivate why the problem is interesting. The "edit" link below the Question can be used to improve it.
– hardmath
Jul 29 '15 at 11:59
A geometric sequence is something like $a, ar, ar^2, ar^3, ldots$. There are no such things to be seen anywhere in this problem.
– David K
Jul 29 '15 at 12:56
Maybe you can get extra credit for proving the geometry in the diagram is wrong. It is not possible to have two 32-degree circular arcs of length 14.4 and 20.25 such that the difference between their radii is 13. Why?
– David K
Jul 29 '15 at 13:16
@DavidK The discovery that the data are not consistent is nice. Would like to know “was the inconsistency found by full computations or by noticing some irregularities of the combination of numbers”?
– Mick
Jul 29 '15 at 14:08
@Mick I forget the exact moment I noticed this, but I think it was while contemplating the radius of the 14.4-meter arc. The four measurements are redundant (any three of them would be sufficient to compute the fourth measurement and also compute $r$). Where you have redundancy you have a chance for inconsistency. It also seemed that there should be a factor of $pi$ (or at least an approximation of it) in at least one measurement, and it seemed to be missing.
– David K
Jul 29 '15 at 19:18
|
show 1 more comment
up vote
1
down vote
favorite
up vote
1
down vote
favorite
A circular stadium consists of sections as illustrated, with aisles in between. The diagram show the tiers of concrete steps for the final section, Section K. Seats are to be place along every step, with each seat being 0.45cm wide. AB, the arc at the front of the first row is 14.4m long, while CD, the arc at the back of the back row is 20.25m long.
$hspace{2in}$
1) How wide is each concrete step?
2) What is the length of the arc of the back of Row 1, Row 2, Row 3, etc.?
3) How many seats are there in Row 1, Row 2, Row 3, ……, Row 13?
4) How many sections are there in the stadium?
5) What is the total seating capacity of the stadium?
6) What is the radius of the ‘playing surface'?
sequences-and-series geometry
edited Jul 29 '15 at 12:37
David K
51.8k340114
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
A circular stadium consists of sections as illustrated, with aisles in between. The diagram show the tiers of concrete steps for the final section, Section K. Seats are to be place along every step, with each seat being 0.45cm wide. AB, the arc at the front of the first row is 14.4m long, while CD, the arc at the back of the back row is 20.25m long.
$hspace{2in}$
1) How wide is each concrete step?
2) What is the length of the arc of the back of Row 1, Row 2, Row 3, etc.?
3) How many seats are there in Row 1, Row 2, Row 3, ……, Row 13?
4) How many sections are there in the stadium?
5) What is the total seating capacity of the stadium?
6) What is the radius of the ‘playing surface'?
sequences-and-series geometry
sequences-and-series geometry
edited Jul 29 '15 at 12:37
David K
51.8k340114
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
edited Jul 29 '15 at 12:37
David K
51.8k340114
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
edited Jul 29 '15 at 12:37
David K
51.8k340114
edited Jul 29 '15 at 12:37
David K
51.8k340114
edited Jul 29 '15 at 12:37
David K
51.8k340114
51.8k340114
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
asked Jul 29 '15 at 11:51
MathEnthusiast4060225
63
63
Welcome to Math.SE! Please review How to Ask for ways to improve your Question. As it currently reads, you have multiple parts with no indication of where you may be having difficulty, and there's no context to motivate why the problem is interesting. The "edit" link below the Question can be used to improve it.
– hardmath
Jul 29 '15 at 11:59
A geometric sequence is something like $a, ar, ar^2, ar^3, ldots$. There are no such things to be seen anywhere in this problem.
– David K
Jul 29 '15 at 12:56
Maybe you can get extra credit for proving the geometry in the diagram is wrong. It is not possible to have two 32-degree circular arcs of length 14.4 and 20.25 such that the difference between their radii is 13. Why?
– David K
Jul 29 '15 at 13:16
@DavidK The discovery that the data are not consistent is nice. Would like to know “was the inconsistency found by full computations or by noticing some irregularities of the combination of numbers”?
– Mick
Jul 29 '15 at 14:08
@Mick I forget the exact moment I noticed this, but I think it was while contemplating the radius of the 14.4-meter arc. The four measurements are redundant (any three of them would be sufficient to compute the fourth measurement and also compute $r$). Where you have redundancy you have a chance for inconsistency. It also seemed that there should be a factor of $pi$ (or at least an approximation of it) in at least one measurement, and it seemed to be missing.
– David K
Jul 29 '15 at 19:18
|
show 1 more comment
Welcome to Math.SE! Please review How to Ask for ways to improve your Question. As it currently reads, you have multiple parts with no indication of where you may be having difficulty, and there's no context to motivate why the problem is interesting. The "edit" link below the Question can be used to improve it.
– hardmath
Jul 29 '15 at 11:59
A geometric sequence is something like $a, ar, ar^2, ar^3, ldots$. There are no such things to be seen anywhere in this problem.
– David K
Jul 29 '15 at 12:56
Maybe you can get extra credit for proving the geometry in the diagram is wrong. It is not possible to have two 32-degree circular arcs of length 14.4 and 20.25 such that the difference between their radii is 13. Why?
– David K
Jul 29 '15 at 13:16
@DavidK The discovery that the data are not consistent is nice. Would like to know “was the inconsistency found by full computations or by noticing some irregularities of the combination of numbers”?
– Mick
Jul 29 '15 at 14:08
@Mick I forget the exact moment I noticed this, but I think it was while contemplating the radius of the 14.4-meter arc. The four measurements are redundant (any three of them would be sufficient to compute the fourth measurement and also compute $r$). Where you have redundancy you have a chance for inconsistency. It also seemed that there should be a factor of $pi$ (or at least an approximation of it) in at least one measurement, and it seemed to be missing.
– David K
Jul 29 '15 at 19:18
Welcome to Math.SE! Please review How to Ask for ways to improve your Question. As it currently reads, you have multiple parts with no indication of where you may be having difficulty, and there's no context to motivate why the problem is interesting. The "edit" link below the Question can be used to improve it.
– hardmath
Jul 29 '15 at 11:59
Welcome to Math.SE! Please review How to Ask for ways to improve your Question. As it currently reads, you have multiple parts with no indication of where you may be having difficulty, and there's no context to motivate why the problem is interesting. The "edit" link below the Question can be used to improve it.
– hardmath
Jul 29 '15 at 11:59
A geometric sequence is something like $a, ar, ar^2, ar^3, ldots$. There are no such things to be seen anywhere in this problem.
– David K
Jul 29 '15 at 12:56
A geometric sequence is something like $a, ar, ar^2, ar^3, ldots$. There are no such things to be seen anywhere in this problem.
– David K
Jul 29 '15 at 12:56
Maybe you can get extra credit for proving the geometry in the diagram is wrong. It is not possible to have two 32-degree circular arcs of length 14.4 and 20.25 such that the difference between their radii is 13. Why?
– David K
Jul 29 '15 at 13:16
Maybe you can get extra credit for proving the geometry in the diagram is wrong. It is not possible to have two 32-degree circular arcs of length 14.4 and 20.25 such that the difference between their radii is 13. Why?
– David K
Jul 29 '15 at 13:16
@DavidK The discovery that the data are not consistent is nice. Would like to know “was the inconsistency found by full computations or by noticing some irregularities of the combination of numbers”?
– Mick
Jul 29 '15 at 14:08
@DavidK The discovery that the data are not consistent is nice. Would like to know “was the inconsistency found by full computations or by noticing some irregularities of the combination of numbers”?
– Mick
Jul 29 '15 at 14:08
@Mick I forget the exact moment I noticed this, but I think it was while contemplating the radius of the 14.4-meter arc. The four measurements are redundant (any three of them would be sufficient to compute the fourth measurement and also compute $r$). Where you have redundancy you have a chance for inconsistency. It also seemed that there should be a factor of $pi$ (or at least an approximation of it) in at least one measurement, and it seemed to be missing.
– David K
Jul 29 '15 at 19:18
@Mick I forget the exact moment I noticed this, but I think it was while contemplating the radius of the 14.4-meter arc. The four measurements are redundant (any three of them would be sufficient to compute the fourth measurement and also compute $r$). Where you have redundancy you have a chance for inconsistency. It also seemed that there should be a factor of $pi$ (or at least an approximation of it) in at least one measurement, and it seemed to be missing.
– David K
Jul 29 '15 at 19:18
|
show 1 more comment
1 Answer
1
active
oldest
votes
up vote
0
down vote
First of im new here.
but the answer to question number one whould be (without actually writing all the numbers) The first step is obviously 14.4m wide and every step afther that is the widht of the one before him incremented by 0.45 ending with step 13 with a width of 20.25m
The calculation : (20.25 - 14.4) / 13
The answer of the 3th question whould be starting with row one 32 seats every row has one seat more then the one in front of it there fore the last one has 44 seats
The answer to the 4th question : One section is 32 degrees we need a circle so 360degrees therefore 11 sections
The answer to the 5th question : (i solved this one by writing a small java program) while (i < 13) {a++} ans = 11 * a
The answer then becomes 5577 seats
I believe the answer to the 6th question whould be like this : ((11 * 14.4) / pi) / 2 = 50.4
I have not yet learned latex im working on that :)
answered Jul 29 '15 at 12:13
Delano Zuurman
13
Sometimes it's better to just do the math in a more "traditional" way, because there's obviously an error in how you programmed the question in Java and your use of the computer offers no easy way to detect the error. A little "traditional" math, however, says that if you know you have 32 seats per section in the first row, and 11 sections, that's already 352 seats. And the other rows have more. By the time you count up the first three rows you already have more than 934 seats, so that is not even close to the total capacity.
– David K
Jul 29 '15 at 12:46
Yes you are absolutely correct its a stupid mistake as well, though the error is easy. by doing a++ i incremented a by one instead of taking 32 + 33 etc. Thank you for this correction.
– Delano Zuurman
Jul 29 '15 at 12:48
For those intrested in the java code i did it like this : package maths; public class math { public static void main(String args) { Integer i = 0; Integer a = 32; Integer seats = 0; while(i < 13) { a++; seats += a; i++; } Integer answer = seats * 11; System.out.println(answer); } }
– Delano Zuurman
Jul 29 '15 at 12:58
I was going to make another "correction" but then realized the question is underspecified: does each seat "occupy" an arc length of 45 cm along the front of the row, or along the back of the row? If it's measured along the back of the row then you get an extra seat for each row in each section.
– David K
Jul 29 '15 at 13:08
Could you explain to me how that works ? if its the front of the row it gets 1 extra seat but in the back 2 ?
– Delano Zuurman
Jul 29 '15 at 13:12
|
show 2 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
First of im new here.
but the answer to question number one whould be (without actually writing all the numbers) The first step is obviously 14.4m wide and every step afther that is the widht of the one before him incremented by 0.45 ending with step 13 with a width of 20.25m
The calculation : (20.25 - 14.4) / 13
The answer of the 3th question whould be starting with row one 32 seats every row has one seat more then the one in front of it there fore the last one has 44 seats
The answer to the 4th question : One section is 32 degrees we need a circle so 360degrees therefore 11 sections
The answer to the 5th question : (i solved this one by writing a small java program) while (i < 13) {a++} ans = 11 * a
The answer then becomes 5577 seats
I believe the answer to the 6th question whould be like this : ((11 * 14.4) / pi) / 2 = 50.4
I have not yet learned latex im working on that :)
answered Jul 29 '15 at 12:13
Delano Zuurman
13
Sometimes it's better to just do the math in a more "traditional" way, because there's obviously an error in how you programmed the question in Java and your use of the computer offers no easy way to detect the error. A little "traditional" math, however, says that if you know you have 32 seats per section in the first row, and 11 sections, that's already 352 seats. And the other rows have more. By the time you count up the first three rows you already have more than 934 seats, so that is not even close to the total capacity.
– David K
Jul 29 '15 at 12:46
Yes you are absolutely correct its a stupid mistake as well, though the error is easy. by doing a++ i incremented a by one instead of taking 32 + 33 etc. Thank you for this correction.
– Delano Zuurman
Jul 29 '15 at 12:48
For those intrested in the java code i did it like this : package maths; public class math { public static void main(String args) { Integer i = 0; Integer a = 32; Integer seats = 0; while(i < 13) { a++; seats += a; i++; } Integer answer = seats * 11; System.out.println(answer); } }
– Delano Zuurman
Jul 29 '15 at 12:58
I was going to make another "correction" but then realized the question is underspecified: does each seat "occupy" an arc length of 45 cm along the front of the row, or along the back of the row? If it's measured along the back of the row then you get an extra seat for each row in each section.
– David K
Jul 29 '15 at 13:08
Could you explain to me how that works ? if its the front of the row it gets 1 extra seat but in the back 2 ?
– Delano Zuurman
Jul 29 '15 at 13:12
|
show 2 more comments
up vote
0
down vote
First of im new here.
but the answer to question number one whould be (without actually writing all the numbers) The first step is obviously 14.4m wide and every step afther that is the widht of the one before him incremented by 0.45 ending with step 13 with a width of 20.25m
The calculation : (20.25 - 14.4) / 13
The answer of the 3th question whould be starting with row one 32 seats every row has one seat more then the one in front of it there fore the last one has 44 seats
The answer to the 4th question : One section is 32 degrees we need a circle so 360degrees therefore 11 sections
The answer to the 5th question : (i solved this one by writing a small java program) while (i < 13) {a++} ans = 11 * a
The answer then becomes 5577 seats
I believe the answer to the 6th question whould be like this : ((11 * 14.4) / pi) / 2 = 50.4
I have not yet learned latex im working on that :)
answered Jul 29 '15 at 12:13
Delano Zuurman
13
Sometimes it's better to just do the math in a more "traditional" way, because there's obviously an error in how you programmed the question in Java and your use of the computer offers no easy way to detect the error. A little "traditional" math, however, says that if you know you have 32 seats per section in the first row, and 11 sections, that's already 352 seats. And the other rows have more. By the time you count up the first three rows you already have more than 934 seats, so that is not even close to the total capacity.
– David K
Jul 29 '15 at 12:46
Yes you are absolutely correct its a stupid mistake as well, though the error is easy. by doing a++ i incremented a by one instead of taking 32 + 33 etc. Thank you for this correction.
– Delano Zuurman
Jul 29 '15 at 12:48
For those intrested in the java code i did it like this : package maths; public class math { public static void main(String args) { Integer i = 0; Integer a = 32; Integer seats = 0; while(i < 13) { a++; seats += a; i++; } Integer answer = seats * 11; System.out.println(answer); } }
– Delano Zuurman
Jul 29 '15 at 12:58
I was going to make another "correction" but then realized the question is underspecified: does each seat "occupy" an arc length of 45 cm along the front of the row, or along the back of the row? If it's measured along the back of the row then you get an extra seat for each row in each section.
– David K
Jul 29 '15 at 13:08
Could you explain to me how that works ? if its the front of the row it gets 1 extra seat but in the back 2 ?
– Delano Zuurman
Jul 29 '15 at 13:12
|
show 2 more comments
up vote
0
down vote
up vote
0
down vote
First of im new here.
but the answer to question number one whould be (without actually writing all the numbers) The first step is obviously 14.4m wide and every step afther that is the widht of the one before him incremented by 0.45 ending with step 13 with a width of 20.25m
The calculation : (20.25 - 14.4) / 13
The answer of the 3th question whould be starting with row one 32 seats every row has one seat more then the one in front of it there fore the last one has 44 seats
The answer to the 4th question : One section is 32 degrees we need a circle so 360degrees therefore 11 sections
The answer to the 5th question : (i solved this one by writing a small java program) while (i < 13) {a++} ans = 11 * a
The answer then becomes 5577 seats
I believe the answer to the 6th question whould be like this : ((11 * 14.4) / pi) / 2 = 50.4
I have not yet learned latex im working on that :)
answered Jul 29 '15 at 12:13
Delano Zuurman
13
First of im new here.
but the answer to question number one whould be (without actually writing all the numbers) The first step is obviously 14.4m wide and every step afther that is the widht of the one before him incremented by 0.45 ending with step 13 with a width of 20.25m
The calculation : (20.25 - 14.4) / 13
The answer of the 3th question whould be starting with row one 32 seats every row has one seat more then the one in front of it there fore the last one has 44 seats
The answer to the 4th question : One section is 32 degrees we need a circle so 360degrees therefore 11 sections
The answer to the 5th question : (i solved this one by writing a small java program) while (i < 13) {a++} ans = 11 * a
The answer then becomes 5577 seats
I believe the answer to the 6th question whould be like this : ((11 * 14.4) / pi) / 2 = 50.4
I have not yet learned latex im working on that :)
answered Jul 29 '15 at 12:13
Delano Zuurman
13
edited Jul 29 '15 at 12:57
answered Jul 29 '15 at 12:13
Delano Zuurman
13
answered Jul 29 '15 at 12:13
Delano Zuurman
13
answered Jul 29 '15 at 12:13
Delano Zuurman
13
13
Sometimes it's better to just do the math in a more "traditional" way, because there's obviously an error in how you programmed the question in Java and your use of the computer offers no easy way to detect the error. A little "traditional" math, however, says that if you know you have 32 seats per section in the first row, and 11 sections, that's already 352 seats. And the other rows have more. By the time you count up the first three rows you already have more than 934 seats, so that is not even close to the total capacity.
– David K
Jul 29 '15 at 12:46
Yes you are absolutely correct its a stupid mistake as well, though the error is easy. by doing a++ i incremented a by one instead of taking 32 + 33 etc. Thank you for this correction.
– Delano Zuurman
Jul 29 '15 at 12:48
For those intrested in the java code i did it like this : package maths; public class math { public static void main(String args) { Integer i = 0; Integer a = 32; Integer seats = 0; while(i < 13) { a++; seats += a; i++; } Integer answer = seats * 11; System.out.println(answer); } }
– Delano Zuurman
Jul 29 '15 at 12:58
I was going to make another "correction" but then realized the question is underspecified: does each seat "occupy" an arc length of 45 cm along the front of the row, or along the back of the row? If it's measured along the back of the row then you get an extra seat for each row in each section.
– David K
Jul 29 '15 at 13:08
Could you explain to me how that works ? if its the front of the row it gets 1 extra seat but in the back 2 ?
– Delano Zuurman
Jul 29 '15 at 13:12
|
show 2 more comments
Sometimes it's better to just do the math in a more "traditional" way, because there's obviously an error in how you programmed the question in Java and your use of the computer offers no easy way to detect the error. A little "traditional" math, however, says that if you know you have 32 seats per section in the first row, and 11 sections, that's already 352 seats. And the other rows have more. By the time you count up the first three rows you already have more than 934 seats, so that is not even close to the total capacity.
– David K
Jul 29 '15 at 12:46
Yes you are absolutely correct its a stupid mistake as well, though the error is easy. by doing a++ i incremented a by one instead of taking 32 + 33 etc. Thank you for this correction.
– Delano Zuurman
Jul 29 '15 at 12:48
For those intrested in the java code i did it like this : package maths; public class math { public static void main(String args) { Integer i = 0; Integer a = 32; Integer seats = 0; while(i < 13) { a++; seats += a; i++; } Integer answer = seats * 11; System.out.println(answer); } }
– Delano Zuurman
Jul 29 '15 at 12:58
I was going to make another "correction" but then realized the question is underspecified: does each seat "occupy" an arc length of 45 cm along the front of the row, or along the back of the row? If it's measured along the back of the row then you get an extra seat for each row in each section.
– David K
Jul 29 '15 at 13:08
Could you explain to me how that works ? if its the front of the row it gets 1 extra seat but in the back 2 ?
– Delano Zuurman
Jul 29 '15 at 13:12
Sometimes it's better to just do the math in a more "traditional" way, because there's obviously an error in how you programmed the question in Java and your use of the computer offers no easy way to detect the error. A little "traditional" math, however, says that if you know you have 32 seats per section in the first row, and 11 sections, that's already 352 seats. And the other rows have more. By the time you count up the first three rows you already have more than 934 seats, so that is not even close to the total capacity.
– David K
Jul 29 '15 at 12:46
Sometimes it's better to just do the math in a more "traditional" way, because there's obviously an error in how you programmed the question in Java and your use of the computer offers no easy way to detect the error. A little "traditional" math, however, says that if you know you have 32 seats per section in the first row, and 11 sections, that's already 352 seats. And the other rows have more. By the time you count up the first three rows you already have more than 934 seats, so that is not even close to the total capacity.
– David K
Jul 29 '15 at 12:46
Yes you are absolutely correct its a stupid mistake as well, though the error is easy. by doing a++ i incremented a by one instead of taking 32 + 33 etc. Thank you for this correction.
– Delano Zuurman
Jul 29 '15 at 12:48
Yes you are absolutely correct its a stupid mistake as well, though the error is easy. by doing a++ i incremented a by one instead of taking 32 + 33 etc. Thank you for this correction.
– Delano Zuurman
Jul 29 '15 at 12:48
For those intrested in the java code i did it like this : package maths; public class math { public static void main(String args) { Integer i = 0; Integer a = 32; Integer seats = 0; while(i < 13) { a++; seats += a; i++; } Integer answer = seats * 11; System.out.println(answer); } }
– Delano Zuurman
Jul 29 '15 at 12:58
For those intrested in the java code i did it like this : package maths; public class math { public static void main(String args) { Integer i = 0; Integer a = 32; Integer seats = 0; while(i < 13) { a++; seats += a; i++; } Integer answer = seats * 11; System.out.println(answer); } }
– Delano Zuurman
Jul 29 '15 at 12:58
I was going to make another "correction" but then realized the question is underspecified: does each seat "occupy" an arc length of 45 cm along the front of the row, or along the back of the row? If it's measured along the back of the row then you get an extra seat for each row in each section.
– David K
Jul 29 '15 at 13:08
I was going to make another "correction" but then realized the question is underspecified: does each seat "occupy" an arc length of 45 cm along the front of the row, or along the back of the row? If it's measured along the back of the row then you get an extra seat for each row in each section.
– David K
Jul 29 '15 at 13:08
Could you explain to me how that works ? if its the front of the row it gets 1 extra seat but in the back 2 ?
– Delano Zuurman
Jul 29 '15 at 13:12
Could you explain to me how that works ? if its the front of the row it gets 1 extra seat but in the back 2 ?
– Delano Zuurman
Jul 29 '15 at 13:12
|
show 2 more comments
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Welcome to Math.SE! Please review How to Ask for ways to improve your Question. As it currently reads, you have multiple parts with no indication of where you may be having difficulty, and there's no context to motivate why the problem is interesting. The "edit" link below the Question can be used to improve it.
– hardmath
Jul 29 '15 at 11:59
A geometric sequence is something like $a, ar, ar^2, ar^3, ldots$. There are no such things to be seen anywhere in this problem.
– David K
Jul 29 '15 at 12:56
Maybe you can get extra credit for proving the geometry in the diagram is wrong. It is not possible to have two 32-degree circular arcs of length 14.4 and 20.25 such that the difference between their radii is 13. Why?
– David K
Jul 29 '15 at 13:16
@DavidK The discovery that the data are not consistent is nice. Would like to know “was the inconsistency found by full computations or by noticing some irregularities of the combination of numbers”?
– Mick
Jul 29 '15 at 14:08
@Mick I forget the exact moment I noticed this, but I think it was while contemplating the radius of the 14.4-meter arc. The four measurements are redundant (any three of them would be sufficient to compute the fourth measurement and also compute $r$). Where you have redundancy you have a chance for inconsistency. It also seemed that there should be a factor of $pi$ (or at least an approximation of it) in at least one measurement, and it seemed to be missing.
– David K
Jul 29 '15 at 19:18