關於 sum meaning ，我們在網路上蒐集到這些相關的討論、資訊與評價

This video got us all speechless. But we will sum it up with one word. PARADISE. 😍

#Repost IG: @the.ark.team
📍 Layang Layang Island

𝗗𝗜𝗩𝗘 𝗦𝗜𝗧𝗘 𝗛𝗜𝗚𝗛𝗟𝗜𝗚𝗛𝗧:
𝗧𝗛𝗘 𝗣𝗢𝗜𝗡𝗧, 𝗟𝗔𝗬𝗔𝗡𝗚 𝗟𝗔𝗬𝗔𝗡𝗚 𝗜𝗦𝗟𝗔𝗡𝗗

The convergence of two dive sites, Gorgonian Forest and Dogtooth Lair, forms a sharp corner that we call The Point. It is a gradual slope from 5m to 18m, then a steep slope down into the abyss. The currents here can be tricky at times, but this is where we usually hunt for hammerheads. Sometimes, we would leave early (6 or 7am) to increase our chances of hammerhead sightings. Depending on the current, we would drop in at the top of the reef at 5m, then slowly descend to 20m as we head out into the blue (meaning away from the reef) in search of the sharks. We would spend about 10-15mins out there, and if we find what we're looking for, we'd stay there as long as our no decompression limit allows. After that, we then find our way back to the reef and end the dive with a school of jackfish or barracudas accompanying our safety stop! Sometimes, divers might even see manta rays, eagle rays, and devil rays here. Other marine animals commonly seen here are dogtooth tunas, white tip sharks, and grey reef sharks.

The hammerhead sharks are usually seen out in the blue, but sometimes after coming back to the reef without a single sighting, we'd bump right into a school at the shallow reef! Layang Layang is truly full of surprises.

In the video, you can hear a loud beeping sound: an alarm from our camerawoman's dive computer set to beep at 27m. Being out in the blue with no reference point, it is important to be aware of our depth, especially if we see a school of hammerheads! In our excitement, the last thing we want is accidentally going deeper than our limit.

Video by @krys.uwfilms for The Ark Team
@layanglayangislandresort

📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

ความรู้เรื่องแสงกับการเล่าเรื่องและเครื่องมือเพื่อการสร้างภาษาภาพ

//Admin ทราย

แสงกับการเล่าเรื่อง

การเล่าเรื่องในภาพยนตร์นั้นมีเครื่องมือหลายชนิดที่สามารถใช้ในการสื่อความหมาย
ดังที่เคยกล่าวมาก่อนหน้านี้
https://www.facebook.com/manopapleklek/posts/1281328852020216?__tn__=K-R

และแสงเป็นเครื่องมือสำคัญตัวหนึ่ง ที่ช่วยเล่าเรื่องได้เป็นอย่างดี

การที่เราจะใช้แสง เพื่อการเล่าเรื่องได้ดีนั้น
ขั้นแรกเราต้องเข้าใจก่อนว่าไฟชนิดใดให้คุณภาพแสงแบบไหน
และ แสงชนิดใดให้อารมณ์แบบไหน
เช่น ต้องการแสงแข็งควรใช้ไฟแบบไหน
ต้องการแสงนุ่มควรใช้ไฟแบบไหน หรือดัดแปลงอย่างไร ให้ได้แสงนุ่มแบบที่ต้องการ
แสงเฉพาะจุด ไฟประเภทไหนเหมาะหรือสามารถทำได้ อีกทั้งไฟแบบไหนให้แสงสีอะไร

ต่อไปเราก็ต้องมาศึกษาว่าแสงแบบไหนให้อารมณ์อย่างไร ความรู้สึกอย่างไร
เช่นแสงแข็งให้ความรู้สึกของความดุดัน ตื่นเต้น น่ากลัว ลึกลับ ฯลฯ
แสงนุ่ม ให้ความรู้สึกของความอ่อนหวาน สดใส ร่าเริง
หรือการจัดแสงแบบ hi key ให้อารมณ์อย่างไร
การจัดแสงแบบ low key ให้อารมณ์อย่างไร

หลังจากนั้นก็หาวิธีจัดการกับไฟที่เรามีอยู่ โดยจัดให้ได้ตามอารมณ์ที่ต้องการสื่อความหมาย
โดยหลักๆแล้วการจัดไฟเพื่อให้เล่าเรื่องได้ มักจะขึ้นอยู่กับ
ประเภทของไฟ ชนิดของไฟ ตำแหน่งของไฟ ระดับของไฟ และ ความเข้มของแสง หรือสีของแสง

ทฤษฎีเคยกล่าวไว้ว่า การจัดแสงแบบ hi key เหมาะกับเรื่องราวที่สดใส ร่าเริง อ่อนหวาน ฯลฯ
การจัดแสงแบบ low key เหมาะกับเรื่องราวที่ตื่นเต้น น่ากลัว ลึกลับ ฯลฯ

แต่ถ้าเราลองคิดนอกกรอบล่ะ เช่นอยากถ่ายหนัง hi key ที่ให้ความรู้สึกน่ากล้ว หรือลึกลับบ้าง
เช่นหนังผีหรือหนังฆาตกรรมที่แสงสว่างสดใส หรือ
ถ่ายหนัง low key ให้ดูอบอุ่น สดใส ร่าเริง เช่นหนังรัก romantic บ้างละ
ก็ไม่น่าจะผิด (ไม่อยากใช้คำว่าผิด เพราะการจัดแสงไม่มีผิด นอกจากทิศทาง)
ขึ้นอยู่กับว่าเราสามารถทำให้ผู้ชมเข้าใจและเชื่อในความหมายที่เราต้องการสื่อได้ดีขนาดไหน
และถ้ายิ่งมีความสวยงามเหมาะสมกับฉากนั้นๆด้วยแล้วละก็.. จะยิ่งดีเลิศ....

การที่เราจะจัดแสงให้สื่อความหมายได้นั้น สิ่งที่เราควรรู้หรือศึกษาทำความเข้าใจต่อไปคือ
ภาษาของแสง เช่น เงาและสีที่เกิดจากแสงนั้นๆ เป็นเวลาช่วงไหนของวัน
แสงที่บอกเวลา มีวิธีไหนบ้าง อย่างไร
แสงที่บอกสถานที่ แต่ละสถานที่จะมีบรรยากาศของแสงที่แตกต่างกัน เช่น วัด ผับบาร์ โรงเรียนฯลฯ
แสงที่บอกบรรยากาศ สงบ น่ากลัว ตื่นเต้น
แสงที่บอกอารมณ์ โกรธ รัก เศร้า
และแสงที่ใช้บอกถึงเหตุการ์เดิมๆ ซำ้ๆ เป็นต้น

แสงจากแหล่งกำเนิดแสงแต่ละอย่างก็จะให้สีและบุคลิกของแสงที่แตกต่างกัน
เช่นแสงจากป้ายโฆษณาในเวลากลางคืน
แสงจากกองไฟcamping
แสงจากไฟถนน
แสงจากตะเกียง
แสงจากทีวี ฯลฯ

การสร้างแสงเหล่านี้จะช่วยเล่าเรื่องราวให้คนดูเข้าใจว่าเหตุการณ์นั้นๆเกิดขึ้น ที่ไหน เวลาใด อย่างไร

และสิ่งที่ไม่ควรมองข้ามอีกอย่าง คือ เงา
ซึ่งเงานั้นเกิดได้เพราะมีแสง
ถ้าเปรียบแสงเหมือนสีขาวในการเขียนภาพ
เงาก็คือสีดำในการเขียนภาพนั่นเอง......

ถึงมีคำกล่าวที่ว่า ช่างภาพ เขียนภาพด้วยแสง......
Light with storytelling.

Storytelling in movies has many tools that can be used to communicate meaning.
As previously mentioned.
https://www.facebook.com/manopapleklek/posts/1281328852020216?__tn__=K-R

And light is one important tool to tell stories well.

Our way of using light for storytelling is good.
First step, we need to understand which light quality of light.
And what kind of light gives the mood.
Like hard light. What kind of lights should I use?
Need soft light? What kind of light do you use or how to modify it to get the soft light you want?
Which type of light is suitable or which type of light can be done? Which type of light can be done?

Next, we have to learn what kind of light gives emotion, how it feels.
Such as hard light, give a feeling of wildness, excitement, scary, mysterious, etc.
Soft light gives you the feeling of sweet, bright, cheerfulness.
Or how hi key lighting makes you feel
How emotional is low key lighting?

After that, find a way to handle the fire we have. It's done according to the emotion that we want, media, meaning.
Essentially, the fire arrangement to tell the story is often based on.
Type of fire, type of fire, position of fire, level of fire and intensity of light or color of light.

The theory once said hi key lighting alignment fits bright, cheerful, sweet, etc.
Low key lighting alignment fits exciting stories, scary, mysterious etc.

But if we think outside the box, like, want to film hi key movie that gives a fierce or mysterious feeling.
Such as ghost movies or murder movies that brighten the light?
Filming low key movies to look warm, bright, cheerful, like romantic love movies.
I shouldn't be wrong (I don't want to use the word wrong because there is no wrong
Depends on how well we can make the audience understand and believe the meaning we want the media.
And if there is beauty suitable for that scene, then.. it will be better....

The way we can light up the meaning of media. What we should know or understand is.
The language of light such as shadow and color caused by light. What time of day is it?
How is the light that tells time?
The lighting that tells each location will have a different atmosphere of light such as temple, pub, bar, school etc.
The light that tells the atmosphere is peaceful, scary, exciting.
A light that tells a temper, love, sadness.
And the light that tells about the same old cause, sum, etc.

Light from each light source will give different colors and character of light.
Such as light from billboard at night
Lights from camping camping campfire.
Lights from street lights
The light from the lantern
Lights from tv etc

Creating these lights will help people tell stories about where and when.

And what not to overlook is a shadow.
Shadow can happen because of light.
If you compare white light to write a picture.
Shadow is black to write that photo......

There is a saying that the photographer wrote the picture with light......Translated

Right after Taiwan, we flew straight to Hong Kong where we spent a few days basking it all its HongKongness- meaning cool streets and dim sum. Here are the 4 chapters of the trip.

i. Victoria Peak
ii. Macau
iii. Mong Kok
iv. Disneyland

======================

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Alexandra Village Food Centre is one of the older hawker centres in Singapore and the food is to die for! Follow us on this journey to grab and review some of their more popular dishes!

THANKS FOR WATCHING YA'LL! OPEN ME UP I HAVE STUFF TO SAY!!

I've listed all of the information in the video so pause and screenshot it if you must! Hope you guys enjoy this new series, I've been meaning to start something like this for a while now and I'm really glad it's finally out there!

MY DEEPEST MOST SINCERE APOLOGIES for the shaky camera and audio problems. These will all be resolved by the next episode. If you have any food recommendations, please comment them down below!

x

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Calculus 微積分系列︰ https://www.youtube.com/playlist?list=PLzDe9mOi1K8o2lveHTSM04WAhaGEZE7xB
適合 DSE 無讀 M1, M2，
但上左 U 之後要讀 Calculus 的同學收睇
由最 basic (中三的 level) 教到 pure maths 的 level，
現大致已有以下內容︰
(1) Concept of Differentiation 微分概念
(2) First Principle 基本原理
(3) Rule development 法則證明
(4) Trigonometric skills 三角學技術
(5) Limit 極限
(6) Sandwiches Theorem 迫近定理
(7) Leibniz Theorem 萊布尼茲定理
(8) Logarithmic differentiation 對數求導法
(9) Implicit differentiation 隱函數微分
(10) Differentiation of more than 2 variables 超過2個變數之微分
(11) Differentiation by Calculator 微分計數機功能
(12) Application of Differentiation - curve sketching 微分應用之曲線描繪
(13) Meaning of Integration 積分意義
(14) Rule of Integration 積分法則
(15) Trigonometric rule of Integration 三角積分法則
(16) Exponential, Logarithmic rule of integration 指數、對數積分法則
(17) Integration by Substitution 代換積分法
(18) Integration by Part 分部積分法
(19) Integration Skill : Partial Fraction 積分技術︰部分分式
(20) Integration by Trigonometric Substitution 三角代換積分法
(21) t-formula
(22) Reduction formula 歸約公式
(23) Limit + Summation = Integration 極限 + 連加 = 積分
(24) Application of Integration – Area 積分應用之求面積
(25) Application of Integration – Volume 積分應用之求體積
(26) Application of Integration – Length of curve 積分應用之求曲線長度
(27) Application of Integration – Surface area 積分應用之求表面積
(28) L’ Hospital rule 洛必達定理
(29) Fundamental Theorem of Integral Calculus 微積分基礎原理
(30) Calculus on Physics 微積分於物理上的應用
(31) Calculus on Economics 微積分於經濟上的應用
(32) Calculus on Archeology 微積分於考古學上的應用
之後不斷 updated，大家密切留意
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