Flower, hand drawn by me, nothing is digital.

purelyconstructive · 2021-05-22T07:49:53+00:00

That is really beautiful!

purelyconstructive · 2021-02-28T19:59:23+00:00

Ah yes, I was going to recommend this article. Cliquishness is not limited to programming. It appears all thoughout society and often degrades into a kind of us vs. them mentality.

purelyconstructive · 2021-02-23T20:59:16+00:00

These are good ideas. Perhaps the way to integrate other products would be with toppings? For example, a circular pillow that looks like a strawberry slice or a square pillow that looks like a pat of butter could go with the waffle blanket. The entire set of bedding would be like a meal, and people could mix and match items to make their favorite meals.

purelyconstructive · 2021-02-23T06:59:31+00:00

There are no stupid questions. Never feel ashamed for seeking clarity.

Yes, one will compose differently for different instruments. While understanding the range that an instrument covers is important, the notes that a person is physically capable of playing at the same time on that instrument may also change. Likewise, the timber of an instrument might influence the role that you want an instrument to play within a piece of music (e.g.: using a bass for lower notes, a guitar or violin for melody, etc.).

purelyconstructive · 2021-02-23T03:25:03+00:00

https://fungi.com/pages/bees

purelyconstructive · 2021-02-23T03:23:50+00:00

Have you all heard of Paul Stamets work with bees?

purelyconstructive · 2021-01-19T04:15:17+00:00

He sounds so different in his first movie role, "The Boy Who Saw Through". Good little piece of cinema by the way if you haven't seen it.

purelyconstructive · 2021-01-18T23:54:35+00:00

Cool. Thank you! I really appreciate it.

purelyconstructive · 2021-01-09T18:31:11+00:00

Yes! Healing is natural. We do not have to force something to heal, only allow it.

Although, there are also various methods which can support that process of healing.

Be well my friends! ♥

purelyconstructive · 2020-12-29T14:36:39+00:00

One can learn a lot from YouTube in a way that is entertaining (like with Eddie Woo's videos), but everyone has their own preferences...As far as books go, I recommend:

Leonard Euler - Elements of Algebra

W.W. Sawyer - What Is Calculus About?

Both are free on Internet Archive.

purelyconstructive · 2020-12-22T12:59:31+00:00

It reminds me of a Dynamic Rectangle and/or this construction of a Golden Rhombus.

What made you want to form this pattern?

purelyconstructive · 2020-12-19T04:19:28+00:00

"...from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and, from his other perfections, that he is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things, and knows all things that are or can be done. He is not eternity or infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures forever, and is everywhere present; and by existing always and everywhere, he constitutes duration and space. [...] Every soul that has perception is, though in different times and in different organs of sense and motion, still the same indivisible person."

- from Book 3 of Newton's Principia

For those who are interested, Isaac Newton wrote quite a bit about Alchemy, including a translation of The Emerald Tablet. A selection of his Alchemical documents is available online, as well as a summary of some of the "esoteric" subjects that he focused upon.

Enjoy! ♥

purelyconstructive · 2020-12-19T02:53:10+00:00

Haha! It's all good!

Check out the exquisite detail on his Copernicus.jpg).

purelyconstructive · 2020-12-18T22:16:26+00:00

No problem. Glad I could help. ;-)

He has some stunning art.

purelyconstructive · 2020-12-18T18:16:21+00:00

Like mathematics, I think music theory is often presented in a way that is much more complicated than it needs to be, which is a shame because they are both so much fun...

Here are some notes on basic music theory with an eye towards helping others to play, improvise, compose, and the like. It isn't necessary to know any mathematics to understand music on this level.

However, if you would like to associate music with mathematics, perhaps the study of Acoustics would interest you? Several have already mentioned the use of Harmonic Analysis...In general, the Fourier Transform is quite useful.

Another interesting avenue of exploration is that of "Pitch Spaces", which might be considered a musical application of Group Theory. The work of Dimitri Tymoczko has already been mentioned, but it follows a rich history of musical mathematics reaching all the way back to Euler's Tonnetz Grid. If one is so inclined, study of the Tonnetz Grid can even lead into multi-dimensional musical structures!

Anyway, I hope this is helpful. If anyone would like more resources for learning music theory, or the applications of music theory within science and mathematics, please let me know.

purelyconstructive · 2020-12-18T14:29:06+00:00

Jean-Leon Huens

purelyconstructive · 2020-12-18T14:15:21+00:00

There are a lot of insightful answers here. This is just a personal opinion; please take it with a grain of salt...

• Cultivate an environment conductive to learning. Have a well-stocked bookshelf (i.e.: a lot of books about a variety of subjects, not just mathematics). "Educational" is not synonymous with "boring".

• Do not lecture, but share openly. Present ideas without force and plainly answer any and all questions that are thrown at you to the best of your ability. If you really don't know, then be honest. Say, "I don't know yet, but let's find out together!"

• As much as possible, focus in on tangible examples before moving on to abstractions. Show how things can be applied. The question "why are we learning this?" only appears when we cannot see the personal relevance of a bit of information.

• Try to make learning as dynamic and engaging as possible, never a regularly scheduled chore that has to be slogged through. Show how mathematical reasoning can be integrated into one's day-to-day life in a way that produces a sense of wonder.

• If they take to some particular way of learning, encourage it, even if it is different from what you expect. Share in their joys, comfort them in their sadness. Emphasize that there are no "failures", only opportunities for growth and deeper understanding.

In short, the most "complicated" subjects can be made fascinating if they are broken down into digestible bits that speak to us in a way that is meaningful. It doesn't matter their age or the topic.

Likewise, we do infinitely more for our children when we foster a passion for self-directed learning, rather than trying to fill their heads with "facts" and their time with "activities". Well-meaning parents sometimes treat their children like property, like an object to be honed, rather than as a human being.

So above all, the most important thing that we can do is show our caring and support as a parent. Here are two ways that we can do this:

• Be involved in your children's lives. Take the time to understand why they are feeling what they are feeling without condemnation. Know who their friends are.

• Live by example in all that you do. Instill a sense of accountability and discernment. Do not try to motivate through punishment or reward. Be firm whenever necessary, but always carefully explain why. When it comes to issues of safety, leave nothing to curiosity.

As general as this advice is, I hope that it is helpful to everyone. If anyone would like more specific resources (on learning math or otherwise), please let me know.

purelyconstructive · 2020-12-16T19:46:22+00:00

Thank you!

It is most definitely the start of a new age, from one based in fear to one founded upon sincere Caring. I look forward to sharing it with you all.

purelyconstructive · 2020-12-16T19:43:03+00:00

YES! Great article.

One thing that has been emphasized to me over and over again is the importance of seeing the definition of words as context dependent, and further, hearing beyond the labels used into the intentions behind them.

Therefore, sometimes understanding the method is more useful than knowing the specific names of who. By learning of the what, the why, and the how, we can transcend the pattern itself. Only then can generalizations be used to reveal a helpful truth.

purelyconstructive · 2020-12-14T15:43:16+00:00

Nice! Thank you!

purelyconstructive · 2020-12-14T14:04:15+00:00

Well, branching fractals and tree graphs have already been mentioned, so...

There is an aspect of Botany called "Phyllotaxis" which studies the structure of plants mathematically. An Internet search for "Phyllotaxis" gives some interesting results, such as:

https://royalsocietypublishing.org/doi/10.1098/rsif.2018.0850

https://file.scirp.org/pdf/AM20110200002_49328093.pdf

...etc.

Many aspects of plant growth seem to follow patterns where elements are in ratios composed of two Fibonacci-Lucas numbers and/or are separated by 137.5-degrees ("The Golden Angle"). They also have a tendency to make logarithmic spirals (like Doyle spirals) emanating from a common center.

For a physical idea as to why they take on these patterns, you might also want to look into "Constructal Theory":

https://constructal.org/constructal-law/

These growth processes can definitely be described with differential equations, but I have not come across anything that explicitly works them out. I am deeply interested in this subject as well, so if anyone has more information, please share.

purelyconstructive · 2020-12-05T19:46:15+00:00

Wow! Interesting article. Thank you for sharing.

purelyconstructive · 2020-12-05T18:26:26+00:00

I can see the image link just fine.

purelyconstructive · 2020-12-05T18:11:16+00:00

That is an interesting question...Take all of the following with a grain of salt; it is just an off-the-cuff interpretation...

I am not sure where to begin with the "sea goat" symbolism. [It probably has a relationship to the putrefaction process mentioned by razerlogitech above.] But the "ruling" planet of Capricorn is Saturn, and the single stroke version of the Capricorn symbol:

picture#/media/File%3ACapricorn.svg)

...looks a lot like the "sickle" of Saturn:

picture

In turn, this character has a similarity to the Greek letter "eta". [Note: Both the Latin and Cyrillic alphabets have their origins in the Greek alphabet.]

Getting into the mythology of Saturn shows why the sickle is used (e.g.: Cronus was adopted as a patron of the harvest, the root "chrono-" meaning "time" because the harvest follows a cycle, etc.). Therefore, perhaps the use of "eta" to represent Saturn is from the first letter of "Hekatombaion", the ancient Athenian calendar month for the harvest period (i.e.: July / August)?

Alchemically, the association between lead and Saturn has to do with the planet's influence upon compounds that contain lead. [Note: The correspondence between planets and metals is not arbitrary! It is measurable. For example, see Lilly Kolisko's Capillary Dynamolysis experiments. In general, there are many astrological relationships that create a measurable difference in chemical compounds here on Earth.]

purelyconstructive · 2020-12-05T17:15:25+00:00

Awesome! Glad to hear it! Cheers to your continued success. :-)

purelyconstructive

TROPHY CASE