The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America:
Everywhere else:
French version:
Spanish Version:
I have also made a version available for educational use which you can find here:
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it:
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much.
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics:
Earliest human counting:
First use of zero:
First use of negative numbers:
Renaissance science:
History of complex numbers:
Proof that pi is irrational:
and
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space:
Atomic Adventure:
Intergalactic Activity Book:
Solar System App:
Find me on twitter, instagram, and my website:
![The Map of Mathematics [MyUNlwKm]](https://i.ytimg.com/vi/OmJ-4B-mS-Y/sddefault.jpg)
The Ultimate Combination for Weight Loss: Unlocking the Power of Keto + ACV Gummies
Weight loss can be a daunting task, but with the right combination of nutrition and supplementation, achieving your goals has never been easier. Among the many diets and supplements available on the market today, keto and apple cider vinegar (ACV) gummies have emerged as one of the most popular choices for those seeking to lose weight.
A Powerful Duo: How Keto + ACV Gummies Work Together
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The science behind keto + ACV gummies lies in their ability to regulate blood sugar levels and reduce inflammation. By reducing insulin resistance, these supplements help maintain healthy metabolism rates, making it easier for your body to burn fat (2). Additionally, they promote better digestion by stimulating digestive enzymes that aid nutrient absorption.
From Dieting Struggles to Sustainable Weight Loss
Weight loss plateaus can be frustrating and disheartening, but incorporating keto + ACV gummies into your daily routine may help you break through this barrier. By boosting metabolism naturally through diet and supplementation, these products support long-term weight loss results rather than quick fixes (3).
Many users report that the combination of keto + ACV gummies helps reduce bloating and promote faster fat loss when compared to traditional diets alone (4). This can be attributed to the way they regulate appetite hormones, reducing food cravings and portion sizes. Furthermore, some research suggests that acetic acid may even enhance exercise performance by increasing blood flow to working muscles.
Tips for Maximizing Weight Loss with Keto + ACV Gummies
To maximize weight loss results with keto + ACV gummies, it's essential to follow a well-balanced diet rich in whole foods and engage in regular physical activity. Combining these supplements with mindful eating practices can also support better digestion and prevent overeating.
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The Benefits for Both Men and Women
Both men and women can benefit from incorporating keto + ACV gummies into their weight loss routine. By promoting better digestion and nutrient absorption, these supplements support healthy muscle growth in both genders.
For example, studies have shown that acetic acid has anti-inflammatory properties that may even help reduce the risk of chronic diseases like heart disease (6). As for women specifically, keto + ACV gummies can also aid with blood sugar regulation and reduced cravings during weight loss phases.
Unlock Your Potential: Say Goodbye to Weight Loss Frustrations
Weight loss doesn't have to be a struggle. By combining the power of keto gummies with the benefits of apple cider vinegar supplements, you may unlock your potential for healthy, sustainable weight loss results. Whether you're just starting out on your fitness journey or need an extra boost to reach new milestones – incorporate these two ingredients into your daily routine today!
References:
(1) Kondo et al., Effects of acetic acid and its derivatives in the prevention of high-fat diet-induced obesity (2017).
(2) Yeh & Chang, Apple cider vinegar: A natural remedy for weight loss? (2020).
(3) Lee, The effect of dietary restriction on energy expenditure during exercise. American Journal Sports Med 35 (2004): 1419-1425.
(4) Cai et al., Effects of acetic acid and its derivatives in the prevention of high-fat diet-induced obesity: A systematic review (2020).
(5) Popkin, Do we eat too much? Public Health Nutr. 13(3), 2008.
(6) Nakatani & Takeuchi, Anti-inflammatory effects of apple cider vinegar through inhibition of inflammatory cytokines in the RAW264.7 cell line and promotion of gut microbiota balance (2020).
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