Matsu Posted February 28, 2012 Report Share Posted February 28, 2012 (edited) Just finished doing this IA and thought I'd help people still trying to figure it out! My two cents: The similar triangles part is a bit of a no-brainer, so for anyone still trying to figure out the trigonometry part of this IA, go check out the diagram near the start of this thread and check out the picture with the two isosceles triangles. If you use software like GeoGebra, which I used, to create a midpoint in the smaller triangle and divide the triangle into two using the midpoint, you suddenly have two right triangles. You can then use the software to find the angle of one of the sides and then boom. You should be able to do the rest. edit: Alternatively, you can do what my friend did and derive the value for theta using trigonometry as well.. It really is your choice hehe. That's how I involved technology in my IA though.. Also, it opens the possibility of using a simpler and way easier theorem concerning right triangles :-" (trying to be mysterious so as to not completely give away the answer) Is this too specific? Edited February 28, 2012 by Matsu 2 Reply Link to post Share on other sites More sharing options...
flyfly Posted March 2, 2012 Report Share Posted March 2, 2012 I was wondering what the question meant by "analytic approach". Does it mean by using reasoning using words only or can it include calculations? Reply Link to post Share on other sites More sharing options...
ina Posted March 5, 2012 Report Share Posted March 5, 2012 Could somebody help me with developing a general statement? Is there a possibility of doing this using technology?I've already done the whole excercise using similar triangles and equations of the circles but I have no bloody idea what they actually expect when they ask for one. Reply Link to post Share on other sites More sharing options...
Trust Posted March 6, 2012 Report Share Posted March 6, 2012 Can someone define what general statement means in IB terms? Should I give a basic description of the trend I see within the answer? or should i make an equation? Reply Link to post Share on other sites More sharing options...
Matsu Posted March 6, 2012 Report Share Posted March 6, 2012 I was wondering what the question meant by "analytic approach". Does it mean by using reasoning using words only or can it include calculations?I used calculations based on analysis that I formed while checking out the configuration of the circles. I think you could do it either way, really, but since it's Math, it's probably a bit safer if you use calculations as well. Could somebody help me with developing a general statement? Is there a possibility of doing this using technology?I've already done the whole excercise using similar triangles and equations of the circles but I have no bloody idea what they actually expect when they ask for one.Try to find a method of solution that works, then replace the values you used with a variable. That's a pretty rough way to think of it. As for technology, you can absolutely use it with this IA, or any IA that IB gives out for that matter. I already gave a couple hints in my post above hehe. Reply Link to post Share on other sites More sharing options...
Argy Posted March 13, 2012 Report Share Posted March 13, 2012 Hi, I just started on this IA yesterday. I've found the general formula for step 1 and compared it to the one found in step 2. I was wondering if using a compass and straightedge to aid in doing so would count as an analytic approach.Thanks! Reply Link to post Share on other sites More sharing options...
Classof2013 Posted April 4, 2012 Report Share Posted April 4, 2012 For presenting the circles, will I score lower if my picture is hand-drawn? My teacher said that it was okay to do this and then scan it. I'm not very good with computer programs :/ I will use the TI-84 plus GDC to check other values of r and OP though for sure, I'm okay with that. Will this be seen differently by the IB? Do they prefer pictures drawn on the computer? Any help would be great, thanks guys! Reply Link to post Share on other sites More sharing options...
jbiscuits1 Posted April 7, 2012 Report Share Posted April 7, 2012 (edited) The math portion is ridiculously simple. You can use common sense to gather all of the side lengths and following that use the Law of Cosines to get any angle you want. My only question with this is the general statement that goes with it. Are we expected to have an end result of just 1 statement that can apply to most if not all situations?Nevermind that, I figured out the general statement and whatnot. Can someone link me to a well organized example just for structure purposes? Edited April 7, 2012 by jbiscuits1 Reply Link to post Share on other sites More sharing options...
jbiscuits1 Posted April 7, 2012 Report Share Posted April 7, 2012 Just finished doing this IA and thought I'd help people still trying to figure it out! My two cents: The similar triangles part is a bit of a no-brainer, so for anyone still trying to figure out the trigonometry part of this IA, go check out the diagram near the start of this thread and check out the picture with the two isosceles triangles. If you use software like GeoGebra, which I used, to create a midpoint in the smaller triangle and divide the triangle into two using the midpoint, you suddenly have two right triangles. You can then use the software to find the angle of one of the sides and then boom. You should be able to do the rest. edit: Alternatively, you can do what my friend did and derive the value for theta using trigonometry as well.. It really is your choice hehe. That's how I involved technology in my IA though.. Also, it opens the possibility of using a simpler and way easier theorem concerning right triangles :-" (trying to be mysterious so as to not completely give away the answer) Is this too specific? I'm not sure your method really works. If you do it correctly the triangles come out to no longer even resemble the original picture. Geogebra is really only a program meant to create images to be used for showing, they aren't designed to help find answers. Reply Link to post Share on other sites More sharing options...
jbiscuits1 Posted April 7, 2012 Report Share Posted April 7, 2012 (edited) One more question, is the general statement suppose to be specific to this problem set or should it be applicable to all triangles?On a different note, I have to general statements that both work and get the job done. One is extremely simple, but it doesnt have a solid mathematical explanation, the other one is extremely long and difficult to follow/understand but it has a very nice explanation that actually makes sense and justifies everything about it. Am I better off with the latter of the two? Edited April 7, 2012 by jbiscuits1 Reply Link to post Share on other sites More sharing options...
Danbo Posted April 8, 2012 Report Share Posted April 8, 2012 (edited) Hey everyone I've already read through the previous posts but I'm still stuck on the first task of the IA >< I used a trigonometrical approach to find the length of OP' but I'm really uncertain whether or not I did it correctly because my OP' ends up being smaller than my OP :\ So I don't know if I'm on the right track or not And if so happens that it's supposed to be how I stated before, can anyone give me anyone help me out with getting the general statement? -Edit- Never mind I figured out that I was completely off track Thanks Desy Glau for the hints :] Edited April 8, 2012 by Edwina Wong Reply Link to post Share on other sites More sharing options...
aangel Posted April 8, 2012 Report Share Posted April 8, 2012 You OP' is meant to be smaller... for most values of r and OP. (look at the diagram).I don't think we are allowed to help you that much on your IA. Reply Link to post Share on other sites More sharing options...
Danbo Posted April 8, 2012 Report Share Posted April 8, 2012 You OP' is meant to be smaller... for most values of r and OP. (look at the diagram).I don't think we are allowed to help you that much on your IA. It's alright aangel. I got this! (That is, until I get stuck again ) Thank you so much for the reply, anyway! Reply Link to post Share on other sites More sharing options...
Danbo Posted April 8, 2012 Report Share Posted April 8, 2012 (edited) You OP' is meant to be smaller... for most values of r and OP. (look at the diagram).I don't think we are allowed to help you that much on your IA.Ohh, I just noticed I made a mistake on my first post. What made me worry was not that my OP' was less than my OP. What I meant was that my OP' was less than my P'P. :\ Edited April 8, 2012 by Edwina Wong Reply Link to post Share on other sites More sharing options...
SymphonyOfSouls Posted April 10, 2012 Report Share Posted April 10, 2012 I'm having trouble forming a general statement for OP'. I've found a way to estimate the values of angles P' and A, but...that's about all. I can't see any pattern in the length of OP' and it's really beginning to frustrate me. I've graphed the length for each value of OP, but I'm just lost. Reply Link to post Share on other sites More sharing options...
Classof2013 Posted April 11, 2012 Report Share Posted April 11, 2012 I'm having trouble forming a general statement for OP'. I've found a way to estimate the values of angles P' and A, but...that's about all. I can't see any pattern in the length of OP' and it's really beginning to frustrate me. I've graphed the length for each value of OP, but I'm just lost. If you do not see a pattern between your values of OP' it is probably 1 of these 2 reasons.1. You calculated the value of OP' wrong. The pattern is very easy to see, if you don't see a pattern, maybe you've not got the right numbers2. You have not written the final answers as fractions. Written as fractions the pattern is blatantly obvious. It is not quite as easy to see as a decimal. Try that if you haven't already. 1 Reply Link to post Share on other sites More sharing options...
SymphonyOfSouls Posted April 12, 2012 Report Share Posted April 12, 2012 I'm having trouble forming a general statement for OP'. I've found a way to estimate the values of angles P' and A, but...that's about all. I can't see any pattern in the length of OP' and it's really beginning to frustrate me. I've graphed the length for each value of OP, but I'm just lost. If you do not see a pattern between your values of OP' it is probably 1 of these 2 reasons. 1. You calculated the value of OP' wrong. The pattern is very easy to see, if you don't see a pattern, maybe you've not got the right numbers 2. You have not written the final answers as fractions. Written as fractions the pattern is blatantly obvious. It is not quite as easy to see as a decimal. Try that if you haven't already. Oh. I thought I must have calculated it wrong, so I went back to check my answers and found I'd indeed calculated them correctly, but the value that went into my results table was the sin of P', not the length of OP', hence the trouble Thank you for that! Reply Link to post Share on other sites More sharing options...
DVO Posted April 14, 2012 Report Share Posted April 14, 2012 when it says let OP=2, fine OP' when r=2.3.4. when i reach r=4 one of my angles comes out to be 0 degrees. i think i am drawing the triangle wrong. can some help me by explaining how the triangle should look Reply Link to post Share on other sites More sharing options...
MariusIBDP Posted April 15, 2012 Report Share Posted April 15, 2012 Description level 5 (max) in Criterion C is "The student tests the validity of the general statement by considering further examples".What exactly are 'further examples' in this case? Is it just that you solve this with similarities and trigonometric approach or is it something else? Could somebody direct me, if it's something else? Reply Link to post Share on other sites More sharing options...
Ginaya Posted April 18, 2012 Report Share Posted April 18, 2012 This may be a little redundant, seeing as how I'm not sure if this question has been answered previously, or not; however, I'm not exactly sure what to include in my introduction.Is it somewhat like the HOA IA where one needs to include the question, method, and scope? Reply Link to post Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.