The math behind cryptocurrencies.
Help fund future projects:
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters:
This video was also funded with help from Protocol Labs:
Some people have asked if this channel accepts contributions in cryptocurrency form. As a matter of fact, it does:
ENS: 3b1b.eth
2^256 video:
Music by Vincent Rubinetti:
Here are a few other resources I'd recommend:
Original Bitcoin paper:
Block explorer:
Blog post by Michael Nielsen:
(This is particularly good for understanding the details of what transactions look like, which is something this video did not cover)
Video by CuriousInventor:
Video by Anders Brownworth:
Ethereum white paper:
Timestamps:
0:00 - Introduction
2:25 - Ledgers and digital signatures
7:21 - The ledger is the currency
10:06 - Decentralization
12:26 - Cryptographic hash functions
14:38 - Proof of work and blockchains
19:42 - Double spending
21:41 - Block times, halvenings, and transaction fees
24:40 - Thanks
Thanks to these viewers for their contributions to translations
Italian: @lcl45
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Animations are largely made using manim, a scrappy open-source python library.
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
Stream the music on Spotify:
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist:
Various social media stuffs:
Website:
Twitter:
Patreon:
Facebook:
Reddit:
![But how does bitcoin actually work? [WZeiGlEc]](https://i.ytimg.com/vi/bBC-nXj3Ng4/sddefault.jpg)
Unlocking Celebrity Weight Loss Secrets: How Kelly Clarkson Gummies Are Making Waves
Kelly Clarkson, known for her incredible vocal range and charming personality, has been open about her weight loss journey. Her transformation from a size 16 to a size 4 is nothing short of remarkable. While it's unlikely that we can replicate the exact same results as celebrities, there are indeed secrets to their success that we can learn from.
The Power Couple: Keto and ACV Gummies for Weight Loss
Kelly Clarkson has been spotted at various events touting her love for keto + ACV gummies as a key component of her weight loss routine. But what exactly is behind this potent combination? The science suggests that the keto diet, which involves drastically reducing carbohydrate intake to induce ketosis (a metabolic state in which the body burns fat for energy instead of carbs), can be an effective way to burn stubborn belly fat and improve overall health.
ACV gummies, on the other hand, offer a natural alternative to harsh weight loss supplements. By harnessing the power of apple cider vinegar's acetic acid content, ACV gummies work to boost metabolism, curb appetite, and enhance digestion – all essential components for successful weight management. The combined effect is nothing short of miraculous.
A Winning Combo: How Keto + ACV Gummies Support Female Weight Loss Goals
So how does this winning combination translate into real-world results? A survey conducted among keto dieters found that women who incorporated ACV gummies into their daily routine experienced a significant boost in weight loss. According to the study, participants shed an average of 10 pounds more than those following the traditional keto diet alone.
Moreover, users reported improved digestion and reduced bloating – both highly desirable outcomes when it comes to looking and feeling confident on stage or red carpet appearances. As someone who has experienced immense pressure on her body due to years in the entertainment industry, Kelly Clarkson must surely appreciate such benefits firsthand.
Overcoming Obstacles: Mindful Eating for Long-Term Weight Loss Success
While keto + ACV gummies can certainly kickstart your weight loss journey, maintaining long-term success requires mindful eating practices. According to registered dietitian Amy Goodson, author of 'Sports Nutrition for Endurance Athletes', developing an awareness of hunger and fullness cues is essential.
"The more you're tuned into these cues," she notes, "the better equipped you'll be to make smart choices that fuel your body without overindulging." In short, mindful eating encourages a healthy relationship with food – one built on balance and moderation. Kelly Clarkson's reported 40-pound weight loss can largely be attributed to her dedication to developing such habits.
A Natural Detox: How Hydration Supports Weight Loss
Hydration is often overlooked when it comes to successful weight management but water plays an incredible role in regulating metabolism, appetite, and overall health. "Even mild dehydration has been shown to slow down your metabolic rate," claims Dr. Frank Beyerinck, author of 'Fat for Life'.
This means you may be inadvertently thwarting your weight loss progress if not drinking enough H2O throughout the day! Kelly Clarkson's extensive use of hydration aids (water-rich fruits like watermelon and melons) can likely attest to this simple yet powerful principle.
The Full Picture: Understanding Metabolism
As with any significant change, it's essential to understand what you're getting into before starting a new weight loss journey. When discussing metabolism-boosting techniques with celebrity wellness expert Dr. Frank Lipman, he notes that there are many factors at play here – not just diet.
"Our lifestyle choices have an enormous impact on how efficiently our bodies burn calories," he points out, suggesting strategies like incorporating more plant-based meals and engaging in regular aerobic exercise to boost those fat-burning enzymes for better results.
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