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Theorem: Take a circle, the area of this circle is the same as area of a right triangle that has one leg equal to the radius and one leg equal to the circumference of the circle..
A long time ago in a faraway land people led simple lives by the means of agriculture. There was plenty of food to eat and to be merry. They had roofs on their head and fresh river water flowing nearby. Life seemed perfect but it was not. Every year when the rains 🌂 began, the river nearby would flood into the village and destroy their lands and homes. The people in the village would move to a nearby village for shelter with their cattle. When the rain stopped they used to come back and each time they came back they found their place in destruction. Their houses had to be rebuilt and their lands had to be outlined again. Fights were a common scene on how the outline was before the water washed it away. So the concept of the area came to maintain peace.
Finding areas of lands made with straight lines was easy but how to find the area of a land that is a curve ?
Firstly instead of taking a land made up of crazy curves let's take a land made up of the simplest curve, the circle.Draw a circle and fill in its area. Then divide it into large equal parts and arrange them in a rectangle.
It's not yet a perfect rectangle.So divide the circle in parts and try arranging these sections into a rectangle.You'll get a thing that starts looking like rectangle.
Now as you divide the circle more and more and try to arrange those parts you'll get a more nice rectangle. This more and more is nothing but the concept of limits in calculus.
So the area of the circle is the area of the rectangle.The area of the rectangle is Base×Height. Here the height of the rectangle is the radius of the circle and Base is equal to twice the area of the circle. So cut up the rectangle diagonally and you'll get a right-angled triangle with a Base as the radius of the circle and height as the circumference of a circle.
Dark academia moodboard for a botany student?
Here you go! Hope it’s okay ☺️✨
Send me requests for mood boards or playlists ✨
16.10.2020
Some study notes and the view this morning 🥰✨
1.10.2020
Day 1 - Introduce yourself and tell us what you study!
Hi! I’m Maddie and I’m currently studying Psychology, English Language and Chemistry in Sixth Form (year 12) ☺️✨🦋
17.9.2020 🍓
Chemistry is so hard!! I’m really having to put in extra time in order to understand everything... still! English language is super fun and I love studying the use of language in persuasive text ☺️✨
10.9.20
Psychology is so interesting 😍 I’m so glad I chose it, I’ve been leaarning so much! I got to go on a lovely walk the other day so enjoy a photo I took ☺️✨
🎧 I need to be alone - Girl in red
30.8.2020 🍉
Working on my EPQ ☺️ I’m ordering some new stationary today and I’m really looking forward to it, does anyone have suggestions? ✨🍋
I got GCSE results today!
I was so happy with them, especially after all the stress with the predicted grades ☺️✨💕
Day 72/100 days of productivity ☕️🌿
Today wasn’t great but I still got a lot done! I finally did some writing that I’ve been putting off but the deadline is in a few days and I’m not sure if I’m going to finish in time... it’s really annoying because I really didn’t mean to procrastinate this long :/
21st July - What is the best vacation you have ever been on? (note: does not have to have been during summer)
Ah, October a couple of years ago we went to America and it was amazing, we went to Disneyland and saw my aunts and uncles that live there. There were so many amazing coffee shops and I tried a cake shake which was literally a milkshake blended with a cupcake 🧁 I really enjoyed myself then 💫✨
Day 72/100 days of productivity 🌿🦋✨
Today was okay :) I was feeling super run down so I didn’t get as much done as I’d have liked to but I still accomplished lots from my to do list! I’m going to go to bed early and get up at seven tomorrow in order to get some extra stuff done ☺️
18th July - What do you usually do during the summer?
Well, normally I sleep until noon and do absolutely nothing except eat so I’m hoping to make this summer the exception! I’d really like to be productive and active this summer instead of wasting it away sitting on the sofa. I think I’m doing alright so far! ☺️🌿
Day 71/100 days of productivity ☕️🌙
Today went well! I met up with my friend at the park and I had a really great time. I also tidied my room, worked out and overall had a really productive day. So far I’ve stuck with my new bullet journal and I’m super proud of it, even if it is quite a simple design. ☺️💫
17th July - What is the most important task that you need to complete this summer?
I think it’ll be preparing for sixth form! Normally we’d have had an introductory week at the end of term but due to corona we’ve been left to ourselves aha, so this summer I’ll be getting everything ready and double checking I have everything I need! ☺️💫
Good Morning! I hope everyone’s day is lovely today ☺️☕️✨
Day 70/100 days of productivity ☕️🌙
Finally committed to a paper bullet journal! It looks pretty good so far and I’m super proud! It’s really therapeutic to fill out. I also got most of my jobs done today! There were a few I missed but I’ll get them finished tomorrow ☺️✨☕️
14th July - Have your plans changed at all because of the pandemic?
Yep! I was supposed to do GCSEs this year but those have been forgotten :/ it’s nice to not do exams but it feels kind of anticlimactic and a bit like the work I did for the last two years DIDNT end up being used properly. However! It did mean I got to relax on my birthday instead of revising, every cloud ⛅️ ☺️✨☕️
Day 69/100 days of productivity 🌿🦋
Today went well! I got a ton of stuff done and was really pleased with myself ☺️ I kind of overslept this morning but not by much so I wasnt too thrown off ☺️✨🌿
13th July - What are your plans for this summer?
There’s still a chance we could go on holiday! We booked ours for the very end of August so it’s still possible as long as we take correct procedures. I’ll also try to meet up with friends and get some back to school shopping done ☺️✨
68/100 days of productivity ✨🌿
Had a great day today! I got loads done and I started my bullet journal again! I decided to do it electronically so I didn’t have to spend a lot on getting a new journal / fresh pens / etc. Have you guys got any favourite inspo blogs you love? 🌿✨
67/100 days of productivity 💫🥥
Today was good! I tidied my room, worked out and went mini golfing! I also got through loads of my book (it’s so long but the writing is amazing!) 🍋🌿 I’m thinking of starting my bullet journal again, what do you think? 🍯
66/100 days of productivity 🥥🍋
Today was good! I feel super tired but I got through my to do list and sent a few emails. I’ve been toning down how much I do every day more recently since it’s now the summer and I want to relax, even if we didn’t have the exams we still worked super hard these past two years and it’s nice to not have to deal with any more of that! Have you guys met up with any of your friends in person yet?
66/100 days of productivity 💦⚡️
Today went well! I got through everything on my list and had a lovely morning. I’m making more progress with my book! It’s so long but the writing is amazing so it’s worth it ☺️. How are you guys doing today?
Day 65/100 days of productivity 🌙🌸
Ah, picture on the left is one I took in Mallorca. It was so pretty I saw it and felt I had to post it ☺️. Today I did okay! I’ve been eating healthy and I got through way more of my book. I also flicked through old notes and pre alevel notes in order to refresh myself ☺️✨🍃
Day 64/100 days of productivity ☺️🌿✨
Today was good! I got my workout done early and have started prepping for the new school term early so it’s not all done in a rush. I’ve been budgeting for the next few weeks and have made really great progress on my book. How was today for you guys? 🍋🍃✨
Day 64/100 days of productivity 🌸🍃
Had a better day today but I’m still pretty tired. Did some organising in my room and filled in dates in my diary ready for next year. How have you guys been? ✨🌿
Day 63/100 days of productivity ✨☕️
I read some more of my book today! I absolutely adore Stephen King’s writing. Today kinda sucked. My friend’s upset with me and I’ve been feeling super drained. Idk, I let myself eat kinda unhealthily to make myself a little more comfortable but now I feel guilty aha. Anyways! I hope everyone had a lovely day and make sure you stay hydrated!! ✨☔️☕️
Sun - What are you doing to relax?
It’s late! Oh well, can’t take it back aha ☺️
I love to play animal crossing! It’s such a sweet game and I’m so proud of my island even though it’s still pretty new. I also love to meet up with my friends! The other day we went to the park and got ice cream 🥰🍃✨
(My mum picked me some gorgeous sweet pea flowers which are in the picture, I thought they were so pretty!)
Day 62/100 days of productivity 🍇✨
I got a new plant! It’s this adorable cactus and the plant pot is a little moped and it’s the sweetest thing 😍 I also rewrote my writing notes and did pretty well with everything today! 🍃✨
Day 61/100 days of productivity 🌸🍃
Sorry it’s late! I got everything finished and managed to write the first draft of the booklet for my peer teaching programme ☺️
Day 60/100 days of productivity 🌸🍃✨
Today was good! I didn’t eat as healthy as I’d like to have today but no worries, I got some writing done and designed some characters which is super cool! I also got everything on my to do list sorted ☺️✨🌿
Day 59/100 days of productivity 🥥✨🌾
Today went well! I managed to get some reading done as I’d been neglecting my book lately 🥰 I also started up on learning hiragana again! During GCSEs I forgot about it but with all the free time I had I figured it would be good to begin again ☺️✨🌿
Sat - Where in your house is your favourite place to study?
I love my room, it’s really quiet and I always have my music playing. I’ve recently decorated it a bit more and it’s got this really nice vibe that I love to be in now 🥰✨
Sun - What are you doing to relax?
So I love to have a warm bubble bath or to just watch YouTube. I’ve been doing some creative writing as well since I love to write but it’s mostly watching movies in the bath with a really nice scented bubble mixture 🥰☺️🌸
Day 58/100 days of productivity 🌸🌿
Happy Father’s Day for my British followers! I had a great day with my dad and I squeezed in some maths and chemistry work 🥰