關於 by the same token ，我們在網路上蒐集到這些相關的討論、資訊與評價

📜 [專欄新文章] Gas Efficient Card Drawing in Solidity

✍️ Ping Chen

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

Assign random numbers as the index of newly minted NFTs

Scenario

The fun of generative art NFT projects depends on randomness. The industry standard is “blind box”, where both the images’ serial number and the NFTs’ index are predetermined but will be shifted randomly when the selling period ends. (They call it “reveal”) This approach effectively solves the randomness issue. However, it also requires buyers to wait until the campaign terminates. What if buyers want to know the exact card right away? We’ll need a reliable onchain card drawing solution.

The creator of Astrogator🐊 isn’t a fan of blind boxes; instead, it thinks unpacking cards right after purchase is more interesting.

Spec

When initializing this NFT contract, the creator will determine the total supply of it. And there will be an iterable function that is randomly picking a number from the remaining pool. The number must be in range and must not collide with any existing ones.

Our top priority is accessibility/gas efficiency. Given that gas cost on Ethereum is damn high nowadays, we need an elegant algorithm to control gas expanse at an acceptable range.

Achieving robust randomness isn’t the primary goal here. We assume there’s no strong financial incentive to cheat, so the RNG isn’t specified. Implementers can bring their own source of randomness that they think is good enough.

Implementation

Overview

The implementation is pretty short and straightforward. Imagine there’s an array that contains all remaining(unsold) cards. When drawIndex() is called, it generates a (uniform) random seed to draw a card from the array, shortens the array, and returns the selected card.

Algorithm

Drawing X cards from a deck with the same X amount of cards is equal to shuffling the deck and dealing them sequentially. It’s not a surprise that our algorithm is similar to random shuffling, and the only difference is turning that classic algo into an interactive version.

A typical random shuffle looks like this: for an array with N elements, you randomly pick a number i in (0,N), swap array[0] and array[i], then choose another number i in (1,N), swap array[1] and array[i], and so on. Eventually, you’ll get a mathematically random array in O(N) time.

So, the concept of our random card dealing is the same. When a user mints a new card, the smart contract picks a number in the array as NFT index, then grabs a number from the tail to fill the vacancy, in order to keep the array continuous.

Tweak

Furthermore, as long as the space of the NFT index is known, we don’t need to declare/initialize an array(which is super gas-intensive). Instead, assume there’s such an array that the n-th element is n, we don’t actually initialize it (so it is an array only contains “0”) until the rule is broken.

For the convenience of explanation, let’s call that mapping cache. If cache[i] is empty, it should be interpreted as i instead of 0. On the other hand, when a number is chosen and used, we’ll need to fill it up with another unused number. An intuitive method is to pick a number from the end of the array, since the length of the array is going to decrease by 1.

By doing so, the gas cost in the worst-case scenario is bound to be constant.

Performance and limitation

Comparing with the normal ascending index NFT minting, our random NFT implementation requires two extra SSTORE and one extra SLOAD, which cost 12600 ~ 27600 (5000+20000+2600) excess gas per token minted.

Theoretically, any instantly generated onchain random number is vulnerable. We can restrict contract interaction to mitigate risk. The mitigation is far from perfect, but it is the tradeoff that we have to accept.

ping.eth

Gas Efficient Card Drawing in Solidity was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

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How God Can Bless and Multiply You

“For when God made a promise to Abraham, since he could swear by no one greater, he swore by himself, saying, “Surely blessing I will bless you, and multiplying I will multiply you.” Thus, having patiently endured, he obtained the promise. For men indeed swear by a greater one, and in every dispute of theirs the oath is final for confirmation. In this way God, being determined to show more abundantly to the heirs of the promise the immutability of his counsel, interposed with an oath; that by two immutable things, in which it is impossible for God to lie, we may have a strong encouragement, who have fled for refuge to take hold of the hope set before us. This hope we have as an anchor of the soul, a hope both sure and steadfast and entering into that which is within the veil; where as a forerunner Jesus entered for us, having become a high priest forever after the order of Melchizedek.” (Hebrews‬ ‭6:13-20‬ ‭WEB‬‬)

God wanted Abraham to be absolutely sure that He would bless him, so He swore by Himself.

The truth that is impossible for God to lie and His sworn oath gives us a doubly confident hope of receiving His blessing as the seed of Abraham.

When tough times come, just remember that our God who cannot lie has sworn to bless and multiply you, and He is surely doing it.

Even when the world is floundering and men’s hearts are melting because of fear, we can remain stable and unshaken because Jesus is our anchor. He keeps us in shalom peace and leads us to navigate through any storm.

Right now in Heaven, Jesus our high priest is with the Father, praying for us, representing us before the Father.

Whereas the Levitical priesthood under the Law had curses upon those who disobey God’s laws, Jesus’ priesthood after the order of Melchizedek is one that only bestows blessings.

Melchizedek brought the bread and wine to Abraham, and blessed Abraham. In Christ, we are the seed of Abraham, and we can receive God‘s blessings through the same pattern.

Partaking of the Lord’s Supper is such a precious and important time of our day. As we set aside a minute in our day to proclaim the Lord’s death and what that accomplished for us, we benefit from His victory wrought at the cross.

“The cup of blessing which we bless, isn’t it a sharing of the blood of Christ? The bread which we break, isn’t it a sharing of the body of Christ?” (1 Corinthians‬ ‭10:16‬ ‭WEB‬‬)

The apostle Paul called it “the cup of blessing”. Could it be that when we partake, we receive the fulfillment of God’s oath to bless and multiply us? I believe so.

The blood and body of Christ are full of divine life, and when we receive that, we experience close fellowship and identification with Him. This means “I am as You are.” Whatever Jesus is, you also become and have.

If you are not already making the Lord’s Supper the highlight of every day, I encourage you to prioritize this token of Jesus’ love, and see what wonderful things happen in your life!

God has given us many powerful spiritual weapons in Christ that destroy Satanic strongholds, yokes, and bondages. In “Silencing the Serpent”, you will discover how to emerge victorious in spiritual warfare, and be finally set free from cycles of defeat that have perpetuated in your life. Don’t miss it: https://bit.ly/silence-the-serpent-now

📜 [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

12เจ้าหญิงเริงระบำ - นิทานก่อนนอน - นิทานสำหรับเด็ก - ภาพเคลื่อนไหว - การ์ตูน. นิทานเด็กเรื่องเด็กไทยที่ดีที่สุด. ขอบคุณที่เฝ้าติดตามเรา. สนุกกับวิดีโอของเรา. เรื่องราวของเด็ก ๆ. เรื่องราวก่อนนอนสำหรับเด็ก.

กรุณาสมัครสมาชิกฟรี: https://goo.gl/8Y9WxM

The Twelve Dancing Princesses
Twelve princesses, each more beautiful than the last, sleep in twelve beds in the same room. Every night, their doors are securely locked by their father. But in the morning, their dancing shoes are found to be worn through as if they had been dancing all night. The king, perplexed, asks his daughters to explain, but they refuse. The king then promises his kingdom and each daughter to any man who can discover the princesses' midnight secret within three days and three nights.

A soldier is well received at the palace just as the others had been and indeed, in the evening, the princess royal (the eldest daughter) comes to his chamber and offers him a cup of wine.

...
The twelve princesses happily dance all night until their shoes are worn through and they are obliged to leave. The strange adventure continues on the second and third nights, and everything happens just as before, except that on the third night the soldier carries away a golden cup as a token of where he has been. The twelve princes are put under a curse for as many nights as they danced with the princesses.

https://en.wikipedia.org/wiki/The_Twelve_Dancing_Princesses

เทพนิยายช่องเพื่อดูเรื่องราวก่อนนอนที่ดีที่สุด. ตรวจสอบด้านล่างเลือกเรื่องราวที่คุณชื่นชอบและดูเลย! กรุณาสมัครสมาชิกฟรี: https://goo.gl/8Y9WxM

#นิทานก่อนนอนสําหรับเด็ก

ดูเรื่องราวของเด็ก ๆ ในภาษาอังกฤษ:
https://www.youtube.com/channel/UCOPzf8kf-FUDs32E7F2wGdg

?**เทพนิยายเรื่องเจ้าหญิงสำหรับเด็ก**?

? ราพันเซล (ใหม่) - Rapunzel (new): https://youtu.be/S9JpLTfIlZY

? ซินเดอเรลล่า - Cinderella: https://youtu.be/hEYvUbJqK5c

? ราพันเซล - Rapunzel: https://youtu.be/Uzni3lTBs4Y

? ตเติ้ล เมอร์เมด - Little Mermaid: https://youtu.be/uBlvhsC2dWY

? 12เจ้าหญิงเริงระบำ - The Twelve Dancing Princesses:
https://youtu.be/XL7gFqt1Pq0

? สโนไวท์กับคนแคระทั้งเจ็ด การ์ตูน - Snow White and the Seven Dwarfs : https://youtu.be/_avSDQbkFrE

? โฉมงามกับอสูร - Beauty and the Beast: https://youtu.be/40Vs64i2pvo

? เจ้าหญิงนิทรา - Sleeping Beauty: https://youtu.be/CMdaI64tBfU

? ราชินีหิมะ - Snow Queen: https://youtu.be/gVeDucG5eQk

? องค์หญิงและถั่ว - The Princess and the Pea: https://youtu.be/aKXlsxFd5Ns

? เจ้าชายกบ - The Frog Prince: https://youtu.be/o44BspmI0UE


?** เด็กคลาสสิกเทพนิยาย **?

? เดอะนัทแครกเกอร์ - The Nutcracker: https://youtu.be/RzAt0wAOPpI

? มนุษย์ขนมปังขิง - Gingerbread Man: https://youtu.be/tIzRMIgNz7U

? อลิซท่องแดนมหัศจรรย์ - Alice in Wonderland: https://youtu.be/mcZ7qYqp4h4

? แจ็คผู้ฆ่ายักษ์ - Jack and the Beanstalk: https://youtu.be/ktF_8H5lCaE

? ทัมเบลินา - Thumbelina: https://youtu.be/PX4sNo4vwLw

? และโคมไฟวิเศษ - Aladdin and His Magic Lamp
: https://youtu.be/OmM0rQbRntU

? พินอคคิโอ - Pinocchio: https://youtu.be/0qJGjMK2brs

? ฮันเซลและเกรเทล - Hansel and Gretel: https://youtu.be/vvVxm7BkiHo

? พ่อมดแห่งออซ - Wizard of Oz: https://youtu.be/GqW01mmtTzQ

? ปีเตอร์ แพน - Peter Pan: https://youtu.be/_B_fYw9hs18

? อาถรรพ์วันคริสต์มาส - A Christmas Carol: https://youtu.be/CF9iS15er-M

? เด็กหญิงขายไม้ขีดไฟ - The Little Match Girl: https://youtu.be/A0kJYivsH9Y

? หนูน้อยโกลดิล็อคส์ กับหมีสามตัว - Goldilocks and the Three Bears: https://youtu.be/53yqPLH6uDU

? หนูน้อยหมวกแดง - Little Red Riding Hood: https://youtu.be/NZo6cK98Gak

? อาลีบาบากับโจร 40 คน - Ali Baba and the Forty Thieves: https://youtu.be/Qci0aqZiaS8

? ช่างทำรองเท้าและเอลฟ์ - The Elves and the Shoemaker: https://youtu.be/HdjI4IlSdCo

? เมาคลีลูกหมาป่า - The Jungle Book: https://youtu.be/SLj7H7jLjPk

? พุซ อิน บู๊ทส์ - Puss in Boots: https://youtu.be/JjaPCEQ8FL4

? ไฮดี้ สาวน้อยแห่งเทือกเขาแอลป์ - Heidi : https://youtu.be/34y62-rvIyM

? รัมเพิลสติลสกิน - Rumpelstiltskin: https://youtu.be/Utn0SAXbTl8

? เจ้าชายความสุข - Happy Prince: https://youtu.be/j3JpCkemAZM

? ชุดใหม่ของพระราชา - The Emperor's New Clothes: https://youtu.be/GBKXTx45yGE


?** เรื่องสัตว์ **?

? มด ตั๊กแตน - The Ant and the Grasshopper: https://youtu.be/_70w_isLl3I

? หมาป่าและเด็กเจ็ด - The Wolf and the Seven Little Goats: https://youtu.be/F2arYpYEqhw

? ลูกเป็ดขี้เหร่ - The Ugly Duckling: https://youtu.be/BLuho4UK2-U

? ลูกหมูสามตัว - Three Little Pigs: https://youtu.be/xZyUVm1wT14

? เต่า กระต่าย - The Tortoise and the Hare: https://youtu.be/6rXdIpR5ewU

? ราชสีห์กับหนู - The Lion and The Mouse: https://youtu.be/TkL5wJmePjU

? ไก่แดงแสนขยัน - The Little Red Hen: https://youtu.be/qzYE-zGuEyI

? สุนัขจิ้งจอกกับอีกา - The Fox and The Crow: https://youtu.be/Q2xWNxFYPmI

? หนูในเมืองกับหนูชนบท - The Country Mouse and the City Mouse: https://youtu.be/PkPsfNsVa_w

? นักดนตรีแห่งเบรเมน - Town Musicians of Bremen: https://youtu.be/qV3RF4WlIeM

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