Mathematical Tools Collection



#27

A few weeks ago we had a post of an HP calculator collection (by Olivier), and it got me thinking about posting some items I've collected over the years. Well, here they are. My collection is more eclectic than huge, complete, or HP-specific. Hope there's a few interesting ones in here for you.


Not a fancy website, but here ya go.



Link to Collection


#28

What, no Curta???


#29

$$$$$$$$$$$$$$$$$!!!!!!!!!!!!!!! At least not yet.


#30

... and no Logarithmic Tables Books? They are very cheap! I did use one in high school, as late as 1976 or 1977 :-)

Nice pictures!

Gerson.


#31

Don't get me started on posting math books (and tables, etc). I don't have enough web space for that!! :)


#32

Well, I meant the front page only :-)

By the way, does anyone know where to find samples of old log and trig tables? (The older the better!) I am particularly interested in Levi ben Gerson's (no relative! :-) five-place sine tables (14th century).

Thanks,

Gerson.


Edited: 27 Dec 2006, 7:18 a.m.


#33

Gerson, do you really think this forum is the right place to look for a book such old? Though mathematical d;-)


#34

The book (De sinibus, chordis et arcubus - On Sines, Chords and Arcs) was written in France, in 1342. Perhaps some European library have a copy of the manuscript, but I suspect they don't allow anyone to take it home :-) I tried Google Books but all I could find were references to it.

Regards,

Gerson.


#35

There are efforts underway at various libraries to digitize their holdings of old books, manuscripts, and art work and put them on the Web. If you could identify (via Google?) a library which had a copy of this book, you might ask them if they have such plans (and if they don't, you might suggest that they think about it).


#36

#37

Quote:
... and no Logarithmic Tables Books? They are very cheap! I did use one in high school, as late as 1976 or 1977 ..

I still have the "Mathematical Tables - Ninth Edition" that I purchased as an engineering student in the late 1940's. My copy was printed in 1948 with the earliest copyright listed as 1931. I suspect that you are interested in much earlier dates than that. All I can offer is my father's copy of "University Algebra" by Webster Wells copyrighted in 1880 which has a six place table.

My most unique set of tables is "Numeric Conversion Tables from Octal to Decimal and Decimal to Octal" published in 1959 by American Bosch Arma co.


#38

Mine was published in 1976, no copyright notice. However, my first search result led to a 1958 edition of the same book:

http://www.livronet.com.br/produto.php?estante=0&campo=TITULO&spec=T%C1BUA+DE+LOGARITMOS&x=15&y=5

And this is only three blocks away from home :-)

But I am not interested in printed editions, just in links to a couple of scanned pages. Older editions are interesting because they were prone to errors (which motivated Charles Babbage's researches and eventually led to the fine computing devices we have today).

Thanks for helping,

Gerson.

#39

Slight error: You said HP 16 below the HP 16C on your pictures.


#40

Thanks calcfan. I'm sure that's not the last mistake. ;)

#41

What, no planimeter?

What, not even one TI calculator?


#42

A planimeter is coming up next, I think. Neat little machine that we'll look at in my 4th quarter calc class this year, when looking at Green's theorem. As far as the TI's go, I have about 7 or 8, but for some reason they just don't feel right in putting in yet; too new or something. But, they are the most common calculator in schools. However, I have several students purchasing the HP50g this quarter. :) If I get too many math toys I won't have $$ for the other collections (tube radios, musical instruments, cameras, typewriters, etc). Gotta draw the line somewhere.


#43

Quote:
A planimeter is coming up next, I think. Neat little machine ...

If my memory is correct the planimeter was much more than a "neat little machine". We weren't introduced to the machine in my major of aeronautical engineering back in the 1940's. My roommate who was studying civil engineering told me that the planimeter was an important aid in calculating how to balance the earth movements required in railroad and highway construction.

For a "neat little machine" consider the three-arm protractor.



#44

Palmer; More exzctly, it is used to calcualte area. But of course area times height (in this case average height) = volume so your former roommate was correct. The last time i used one was about 84 or 85.


#45

The planimeter does calculate area by way of a hinged arm and usually a gear or rolling mechanism. When one side of the arm is traced around a closed curve sometimes the wheel rotates, sometimes it just slides. Tracing the entire curve "calculates" the area. What's really a great mathematical marvel is the Hatchet Planimeter. One can be made with simply a 14-inch piece of metal rod (just for example). Make a 90-degree bend 2-inches up at each end (looks like a wide U now). Make a closed curve; draw at least a 12-inch line through region. Place one point of the planimeter on the line and one on the curve. CAREFULLY trace out the curve with out twisting or tipping the planimeter. When finished, measure the distance the other end is from the line and multiply by 10 (the length of the planimeter). Voila, the area. Cartographers (like my father) used these all the time.


#46

???

Chuck, please give me some idea why this shall work. Perhaps I missed the point, but integrating by moving one end of an u-shaped rod around a curve with the other end free sounds a bit strange to me. Thanks in advance for a tiny bit of enlightenment!


#47

Walter; Like many of the more arcane formulea in mathematics and surveying; it works by voodo. This is not work for the faint of heart. Most deeds are filed only after the sacrifice of a chiken by the flinty light of a full moon. You don't even want to know what is needed to draw the average USGS map.


#48

Thanks for your confirmation! In fact, I was suspecting this for this "Hatchet P.", but didn't want to mention "voodoo" in my post for obvious reasons (flame wars etc.). But I should have known - in surveys built on feet and thumbs d;-)

Edited: 29 Dec 2006, 3:09 a.m.

#49

Quote:
Walter; Like many of the more arcane formulea in mathematics and surveying; it works by voodo. This is not work for the faint of heart. Most deeds are filed only after the sacrifice of a chiken by the flinty light of a full moon. You don't even want to know what is needed to draw the average USGS map.

This is the truest message here right now.



Walter, the "why it works?" is the $6mil question. Here's a brief (23 page) explanation I'm reading through



http://arxiv.org/PS_cache/math/pdf/9808/9808070.pdf

I have a little more thinking to do on the matter.

CHUCK

Edited: 30 Dec 2006, 12:40 p.m.

#50

Quote:
Palmer; More exzctly, it is used to calcualte area. But of course area times height (in this case average height) = volume so your former roommate was correct. The last time i used one was about 84 or 85.

One of the nice things that a planimeter does is that it calculates the area as one sign if you traverse the area in one direction and calculates the area as of the opposite sign if you traverse the area in the opposite direction. Now suppose that you have a lake with some islands and want te area of the water only. You can, of course, make separate measurements of the entire area and of the islands and make the subtraction on paper. But you can also make "cuts" from the lake's perimeter to the island's perimeter and remember to go the opposite direction around the island and at the end you will have the area of the water as the planimeter output. All you have to do is remember to be sure to follow the same line of the "cut" as you move from the perimeter of the lake to the perimeter of the island and vice versa.


#51

Wikipedia has (of course) a planimeter article with a picture of the device:

#52

Hello Chuck,

Thanks for mentioning my web effort... Looking at your pages, I've considered the idea to add books and slide rules to my web site. It's still building as of today but I'll try to find the @!#=+ box were the slide rules are stored, picture them and add this stuff to the web site.

As a reminder: My web site link


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