Very good. It helps me to find a proof of Euler's formula without using power series and accessible from A level (I needed it to prove the derivative of sin x )
You can find most of my drawings on instagram.com/mathematics.proofs but since this video is very old, it will be right near the bottom. Hope that helps!
You shouldn't be asking how it is... As you can see, it just is. When OS=1, the proof comes out. If you want to play with the value of OS, you're more than welcome to. The chances are, the same proof will come out, so it's a pointless exercise. Don't take my word for it though... Get a pen and paper and play with its value. You don't need my help to do it.
Your question is a common question, but the least important. When OS=1, the proof comes out. It's all that matters. I'm sure that if you change its value to 2.7189 you'll still get the same proof. If you want your question answered, perform experiments. Don't wait for teachers or so called 'experts' to do your thinking for you. Great maths students play around with proofs and aren't afraid to make mistakes.
I'm someone who's pretty direct. Some people like it, some don't. I won't be making assumptions as to how @Naru Saha reacted to my comments. Since I support free speech, you are entitled to voice your opinions without being censored. This is a channel for everyone and they can respond in whatever manner they'd like to. We're here to talk and share ideas. What you regard as rude may simply be a matter of perspective. ;-)
Enjoy the channel, enjoy the moment and enjoy the maths. I spend my valuable time and energy giving back to people. I don't distort the facts or sugar coat my comments. I have confidence in my followers. They are capable and intelligent. They're here to get something they won't get in classrooms.
Lol. I get this question so often. It just is 1, that's all. Make it whatever you want it to be... You'll end up with the same result. There's nothing special about it being 1. Even if it was pi, you'd still get the same proof. Mathematicians used 1 out of convenience. It really is a pointless question. :-D
I won't be making a video about it, as there is no need to. I'd have nothing to say. You're complicating beyond necessity. In maths and likewise in nature, sometimes you have to accept that things are just the way they are. Sometimes there are no reasons. You do something random and you end up making a discovery. This is one of those things. Take this as an example... We know that gravity exists - but we don't really know why it exists. It's just here and we experiment with it. By experimenting with it, we learn more about it, which enables us to develop technologies such as satellites that orbit around planet Earth. Your question leads to a philosophical dead end. It leads to questions as to why mathematics even exists.
I'll end by saying... Your question is like asking why did sin(A-B)=sin(A)cos(B)-cos(A)sin(B) pop out? Why didn't any other proof pop out? What can I say? Someone, somewhere just experimented with the diagram in the video, and out popped the proof sin(A-B)=sin(A)cos(B)-cos(A)sin(B). It's as simple as that. :-D
I see you have removed 'Amazing' video from the title of your proof. Well done! You have recognized something at least. For those who might be interested see comments below.
This seems a little over-complicated. You can tell that the angle you derive as 90-A in step 3 simply by saying this is an right-angled triangle, and the angle at the bottom left is A.
Ian Sergeant There's nothing complicated about it. It's a short video with a few instructions. Remember, not everyone is as smart as you are. Students will be asking questions. They want to know why certain aspects of this proof are true. Thanks for the feedback anyway.
Ian Sergeant You're more than welcome to set up your own UA-cam channel and start sharing videos. No one is stopping you. 405 subscribers isn't hard to beat.
Hello guys, for those of you who want this proof without the hypotenuse as '1', please download my new document: mathsvideos.net/magick-6-6-fundamental-trigonometric-identities-their-proofs. It costs $2.99 to purchase and some of the proceeds from sales will help me maintain this project and work on more proofs. The more books I can purchase, the more I can develop this channel and MathsVideos.net. BTW, this document is being trialled. If you do purchase it, be sure to leave me some feedback!! Cheers!! :-D Also, if for any reason you are unsatisfied with it - I offer a 30 day money back guarantee.
I give this so-called ‘Amazing’ video (see above), 3 out of 10 for effort. It is meant to be a proof - GRAPHICAL, yet very unfortunately the algebra is performed out of sight of the explanatory diagram, which is such a shame. Ian Sergeant's view that it SEEMS over complicated is absolutely smack-on, but for the word 'SEEMS' which should be replaced by the word 'IS'. I should know. I studied the video with a certain degree of bafflement and bemusement. Steps 1, 2 and 3 are completely unnecessary, as are the introduced angles alpha and beta. It took me some considerable time to grasp what was being driven at. The up-loader rightly says not everyone is as smart as Ian Sergeant. Perhaps I fall into this category. From my lowly perspective, the perpendicular to OT (being PR) forms a right-angled triangle (POR) whose angle at O has already been established as being A. Therefore, the complimentary angle subtended at P must be --- wait for it, wait for it (some very basic trigonometry coming here) --- 90 degrees minus A. What could possibly, possibly, possibly be simpler than that? Thank you Ian Sergeant; at one point I thought it I was the only person who could see this. If students are asking questions as to why certain aspects of this proof are true, then why not make it easy for them to understand, instead of unnecessarily muddying the waters or, to quote the up-loader in his response to Mahua Dey, ‘complicating beyond necessity’?
I've taken no shortcuts. People like it. That's all that matters. I'll say this once again; there are more mathematics channels out there. I don't claim to be the high priest of the subject and I don't pretend that perfection exists. Have a good day. :-)
As my channel is making progress, I've noticed that I am getting more comments like these... It's normal. There will always be unhappy customers. If you try to please the world, you end up pleasing nobody.
You certainly have taken a shortcut in not mentioning why OS =1. Some students do not understand why OS has been set at 1 and have reasonably asked why this it the case. Have a good night's sleep :-) :-)
You're thinking too hard, that's the problem. Relax. And also, I've said this time and time again... It doesn't matter what the hypotenuse is... The same proof will emerge. I've shown this in my e-book "Magick 6". It's something I've explained probably about 20 times - which is why I made the e-book.
Thankusooomuch....such a fruitful channel 🥰
Great explanation , AWESOME
Very simple explanation ....tq ..Sir
Very good. It helps me to find a proof of Euler's formula without using power series and accessible from A level (I needed it to prove the derivative of sin x )
Great to hear! Glad it helped!
No question here, as the proof is crystal clear. I just wanted to say thank you for sharing!
Cheers. Glad you liked it!! :-D
I understand how to derive the formula from the shape, but how do I derive the shape itself? Where does it come from? Thanks for the video!
You can find most of my drawings on instagram.com/mathematics.proofs but since this video is very old, it will be right near the bottom. Hope that helps!
YOUR PROOF IS GOOD BUT HOW DID YOU DRAW THIS DIAGRAM
I can't remember to be honest. Was a very long time ago.
There goes a thumbs-up from me!! Keep doing the good work:)
Nice explanation but how os=1,as you've said in this video.
You shouldn't be asking how it is... As you can see, it just is. When OS=1, the proof comes out. If you want to play with the value of OS, you're more than welcome to. The chances are, the same proof will come out, so it's a pointless exercise. Don't take my word for it though... Get a pen and paper and play with its value. You don't need my help to do it.
Your question is a common question, but the least important. When OS=1, the proof comes out. It's all that matters. I'm sure that if you change its value to 2.7189 you'll still get the same proof. If you want your question answered, perform experiments. Don't wait for teachers or so called 'experts' to do your thinking for you. Great maths students play around with proofs and aren't afraid to make mistakes.
bro that is somewhat rude and discouraging u sholld have written that in order to get the proof easily this assumptoon has been made
I'm someone who's pretty direct. Some people like it, some don't. I won't be making assumptions as to how @Naru Saha reacted to my comments. Since I support free speech, you are entitled to voice your opinions without being censored. This is a channel for everyone and they can respond in whatever manner they'd like to. We're here to talk and share ideas. What you regard as rude may simply be a matter of perspective. ;-)
Enjoy the channel, enjoy the moment and enjoy the maths. I spend my valuable time and energy giving back to people. I don't distort the facts or sugar coat my comments. I have confidence in my followers. They are capable and intelligent. They're here to get something they won't get in classrooms.
Can't we keep d os as os other than 1
Doesn't matter what you turn it into mate, you get the same formula at the end of your trials and tribulations. Call it 'k' if you like.
Thank you very much
Can you make another video to explain why it taken as 1
I would be very helpful if u do that
Lol. I get this question so often. It just is 1, that's all. Make it whatever you want it to be... You'll end up with the same result. There's nothing special about it being 1. Even if it was pi, you'd still get the same proof. Mathematicians used 1 out of convenience. It really is a pointless question. :-D
I won't be making a video about it, as there is no need to. I'd have nothing to say. You're complicating beyond necessity. In maths and likewise in nature, sometimes you have to accept that things are just the way they are. Sometimes there are no reasons. You do something random and you end up making a discovery. This is one of those things. Take this as an example... We know that gravity exists - but we don't really know why it exists. It's just here and we experiment with it. By experimenting with it, we learn more about it, which enables us to develop technologies such as satellites that orbit around planet Earth.
Your question leads to a philosophical dead end. It leads to questions as to why mathematics even exists.
I'll end by saying... Your question is like asking why did sin(A-B)=sin(A)cos(B)-cos(A)sin(B) pop out? Why didn't any other proof pop out? What can I say? Someone, somewhere just experimented with the diagram in the video, and out popped the proof sin(A-B)=sin(A)cos(B)-cos(A)sin(B). It's as simple as that. :-D
okkkk thaxxx for your help see yaa at next video
Easy explanation
Very good exaplations☺☺☺☺☺
Thank you. Glad you liked it. :-)
I see you have removed 'Amazing' video from the title of your proof. Well done! You have recognized something at least. For those who might be interested see comments below.
thanks
Nice
good
This seems a little over-complicated. You can tell that the angle you derive as 90-A in step 3 simply by saying this is an right-angled triangle, and the angle at the bottom left is A.
Ian Sergeant There's nothing complicated about it. It's a short video with a few instructions. Remember, not everyone is as smart as you are. Students will be asking questions. They want to know why certain aspects of this proof are true. Thanks for the feedback anyway.
Ian Sergeant You're more than welcome to set up your own UA-cam channel and start sharing videos. No one is stopping you. 405 subscribers isn't hard to beat.
Y os=1
Hello guys, for those of you who want this proof without the hypotenuse as '1', please download my new document: mathsvideos.net/magick-6-6-fundamental-trigonometric-identities-their-proofs. It costs $2.99 to purchase and some of the proceeds from sales will help me maintain this project and work on more proofs. The more books I can purchase, the more I can develop this channel and MathsVideos.net. BTW, this document is being trialled. If you do purchase it, be sure to leave me some feedback!! Cheers!! :-D Also, if for any reason you are unsatisfied with it - I offer a 30 day money back guarantee.
I give this so-called ‘Amazing’ video (see above), 3 out of 10 for effort. It is meant to be a proof - GRAPHICAL, yet very unfortunately the algebra is performed out of sight of the explanatory diagram, which is such a shame.
Ian Sergeant's view that it SEEMS over complicated is absolutely smack-on, but for the word 'SEEMS' which should be replaced by the word 'IS'. I should know. I studied the video with a certain degree of bafflement and bemusement. Steps 1, 2 and 3 are completely unnecessary, as are the introduced angles alpha and beta. It took me some considerable time to grasp what was being driven at. The up-loader rightly says not everyone is as smart as Ian Sergeant. Perhaps I fall into this category.
From my lowly perspective, the perpendicular to OT (being PR) forms a right-angled triangle (POR) whose angle at O has already been established as being A. Therefore, the complimentary angle subtended at P must be --- wait for it, wait for it (some very basic trigonometry coming here) --- 90 degrees minus A.
What could possibly, possibly, possibly be simpler than that? Thank you Ian Sergeant; at one point I thought it I was the only person who could see this.
If students are asking questions as to why certain aspects of this proof are true, then why not make it easy for them to understand, instead of unnecessarily muddying the waters or, to quote the up-loader in his response to Mahua Dey, ‘complicating beyond necessity’?
I've taken no shortcuts. People like it. That's all that matters. I'll say this once again; there are more mathematics channels out there. I don't claim to be the high priest of the subject and I don't pretend that perfection exists. Have a good day. :-)
As my channel is making progress, I've noticed that I am getting more comments like these... It's normal. There will always be unhappy customers. If you try to please the world, you end up pleasing nobody.
You certainly have taken a shortcut in not mentioning why OS =1. Some students do not understand why OS has been set at 1 and have reasonably asked why this it the case. Have a good night's sleep :-) :-)
You're thinking too hard, that's the problem. Relax. And also, I've said this time and time again... It doesn't matter what the hypotenuse is... The same proof will emerge. I've shown this in my e-book "Magick 6". It's something I've explained probably about 20 times - which is why I made the e-book.
That's the beauty of mathematics... You can manipulate lengths - and the same proofs emerge.
good
Cheers!