The Silver Ratio

[MattcAnderson]

Some may know that the golden ration has the expression (1+sqrt(5))/2.
Fewer know that the silver ratio is simply 1+sqrt(2).

See this Numberphile video about silver ratio.

And don't forget about Wikipedia, as a reference, for this interesting mathematics.

golden ratio

silver ratio

Enjoy.

Regards,
Matt

[Dr Sardonicus]

It seems there is a sequence of "metallic ratios" or metallic means, the n^th being given by the simple continued fraction [n;n,n,n,n,...] which represents

.

The first six have been named for the metals gold, silver, bronze, copper, nickel, and tin.

[rudy235]

Originally Posted by Dr Sardonicus

It seems there is a sequence of "metallic ratios" or metallic means, the n^th being given by the simple continued fraction [n;n,n,n,n,...] which represents

.

The first six have been named for the metals gold, silver, bronze, copper, nickel, and tin.

Bronze is not a metal.

It is actually an alloy made of about 7/8 parts of copper and 1 parts of tin. (weightwise)

Perhaps iron would be a better choice. (or lead)

[kriesel]

Originally Posted by rudy235

Bronze is not a metal.

Bronze and brass and other alloys are metals, including those with minor ingredients considered nonmetallic (carbon, sulfur, phosphorus, nitrogen etc). Most metal used in industry is an intentional alloy. Most of our technology is rife with alloys. If not a metal, what is bronze? Typically not glass, ceramic, stone, or organic. (Some metals can be quenched rapidly from molten into a glassy state, as in contacting a rapidly spinning cold heat sink after departing from a narrow aperture in close proximity. https://en.wikipedia.org/wiki/Amorphous_metal)

https://www.merriam-webster.com/dictionary/metal
https://en.wikipedia.org/wiki/Metal

Astrophysicists however have their own definition. Roughly, any element heavier than helium. Alloys don't occur in live stars.

[a1call]

Also, perhaps appropriate to add:

Metallic hydrogen is a phase of hydrogen in which it behaves like an electrical conductor. This phase was predicted in 1935 on theoretical grounds by Eugene Wigner and Hillard Bell Huntington.[1]

At high pressure and temperatures, metallic hydrogen can exist as a partial liquid rather than a solid, and researchers think it might be present in large quantities in the hot and gravitationally compressed interiors of Jupiter and Saturn, as well as in some exoplanets.[2]

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


And:

As shown on the periodic table of the elements below, the majority of the chemical elements in pure form are classified as metals. It seems appropriate to describe what is meant by "metal" in general terms. This general description is adapted from Shipman, et al. Usually have 1-3 electrons in their outer shell.

http://hyperphysics.phy-astr.gsu.edu...tab/metal.html

And a more definitive quote (BTW, there was a time when brass and bronze were interchangeable terms ):

Brass and bronze are both metal alloys, which means they are a combination of two or more different metals. Brass is composed of copper and zinc, whereas bronze is made up of copper and tin, sometimes with other elements such as phosphorus or aluminium added in.

https://www.wandsworthelectrical.com...m%20added%20in.

ETA: Did not want to initiate another post so:

Originally Posted by Dr Sardonicus

As far as metals to describe "beautiful" means or ratios is concerned, I'd choose platinum over lead any day

One of my favorite metals as well, along with Bismuth and Silver. Platinum is the only known catalyst that can be used in Hydrogen-Fuel-Cells. Which makes you wonder what was the point of spending $M in research into Fuel-Cells when all the researchers knew there is just not enough of the element in the world to ever make Fuel-Cells a viable alternative to anything. At least, no-one talks about them anymore.

Grove showed that a reaction between hydrogen and oxygen with a platinum catalyst could produce a current. At the time, it was simply an interesting phenomenon with unknown practical applications.
....

The simple, emissions-free technology proved a good fit for certain highly specialized applications like space travel. NASA in the late 1950s and 1960s used fuel cells for its manned space missions, refining proton-exchange membrane technology using platinum as a catalyst, which they used in the Gemini program. A Pratt-Whitney subsidiary, later acquired by United Technologies Corp., developed a 1.5-kW fuel cell for use in the Apollo program (Figure 3) and the space shuttle, providing electricity and drinking water for the crews.
.....

By the turn of the century, the prospect of utility-scale fuel cells had largely faded and attention turned to smaller systems, for transportation applications and for distributed power on the customer side of the electric meter. Those two applications continue to dominate, but neither has yet resulted in fuel cells becoming anything other than niche players.

https://www.powermag.com/whatever-ha...to-fuel-cells/

[Dr Sardonicus]

Originally Posted by rudy235

Bronze is not a metal.

I challenge you to justify this statement. Bronze is not an element. The term "metal," though applicable especially to metallic elements, is also generally applicable to any substance that has the usual properties attributed to metals - good heat and electrical conductivity, etc. Metallic alloys are the metallurgist's stock in trade.

Most of the elements in the periodic table are generally considered to be metals. Some of the lighter elements, the "noble gases," and the halogens (with the possible exception of astatine) are about it as far as non-metallic elements go.

But even the lightest element, hydrogen, is thought to become metallic when put under enough pressure. The planet Jupiter is known to have a very powerful magnetic field. AFAIK there is no candidate other than metallic hydrogen for the liquid metal responsible for the dynamo generating that field.

As far as metals to describe "beautiful" means or ratios is concerned, I'd choose platinum over lead any day

[kriesel]

Originally Posted by a1call

Platinum is the only known catalyst that can be used in Hydrogen-Fuel-Cells.

Pt-Ni or Pt-Ni-Cu https://samueli.ucla.edu/longer-last...ve-fuel-cells/
Pt-free Fe-N-C https://www.anl.gov/article/platinum...gen-fuel-cells
reversible fuel cell Pt-Pyrochlore, a composite of platinum and a lead ruthenate pyrochlore https://phys.org/news/2021-10-cataly...l-battery.html
nanotech to stretch the Pt-C https://engineering.jhu.edu/material...-applications/
Pd superior (but that does not do much to help cost or supply) for ethanol fuel cells https://www.sciencedirect.com/scienc...60319915027846
Survey of chemistries and suppliers, note nickel is catalyst in a few https://hyfindr.com/hydrogen-fuel-cell-catalyst/
Hydrogen fuel cells also present a problem of sourcing and storing unreacted hydrogen in sufficient volumetric density, and presents considerable explosion hazard. Ethanol is already in large scale production as fuel and uses atmospheric pressure liquid tanks. My truck can drink that or any blend with gasoline.


Re metals, these folks don't sell pure elements. https://www.metalsupermarkets.com/pr...um-sheet-1100/ (1100 aluminum is ~1% not-aluminum content; 1060 0.6%, 1050 0.5%, etc)

Relatively pure alloys like 99.5% or higher aluminum or soft gold wire can be used as gaskets for sealing metal flanges to ultra high vacuum (~10^-10 Torr) against atmosphere and 120C or greater thermal cycling for bakeouts. Such 0.5mm diameter wire will squash to a thin rectangle cross section ~0.2mm x 1mm between stainless steel flanges, and 4 crossed linear wires will form ultra-high-vacuum-tight rectangular gaskets. One can even hang the wires vertically using 3-mm wide slings of low alloy aluminum thin foil. The bits of aluminum or gold contact weld under high local pressure. The thorough cleaning for ultra high vacuum use promotes wire and foil welding to each other. Although it may also adhere somewhat to the flanges, the chromium oxide on stainless steel prevents a true weld of the gasket materials to the flange, and the delicate formed in place gasket can generally be removed intact. https://en.wikipedia.org/wiki/Cold_welding

[rudy235]

Originally Posted by Dr Sardonicus

As far as metals to describe "beautiful" means or ratios is concerned, I'd choose platinum over lead any day

Yes, of course, anyone would choose platinum over lead and even over iron, I simply did not focus much in the "beautiful" aspect and chose one of the six metals known in antiquity, Au, Ag, Cu, Pb and Fe.
Pt on the other hand was only found (discovered) in the XVIII Century.

I think the desultory aspect of this conversation should fade like hydrogen in the atmosphere.

[a1call]

Originally Posted by kriesel

Survey of chemistries and suppliers, note nickel is catalyst in a few https://hyfindr.com/hydrogen-fuel-cell-catalyst/

Acknowledged with thanks. Hydrogen's volatility has engineering solutions. But let's just keep it at that in this thread.

[Uncwilly]

[MattcAnderson]

*smile* because it is worth it :-)