Grandi's series is an infinite series given by: \[ S = 1 - 1 + 1 - 1 + 1 - 1 + \ldots \] This sequence alternates between 1 and -1. The series was named after the Italian mathematician Francesco Grandi, who studied this series in the early 18th century. ### History and Development 1.
In computer science, particularly in distributed systems and blockchain technology, "consensus" refers to a mechanism that enables multiple nodes (or participants) in a network to agree on a single data value or a state of the system, even if some of the nodes fail or act maliciously. Consensus algorithms are essential for ensuring that all nodes have a consistent view of the data and can reach an agreement despite potential inconsistencies or failures.
The remainder is the amount left over after division when one number cannot be evenly divided by another. It is the part of the dividend that is not evenly distributed into the divisor. For example, in the division of 10 by 3: - 10 divided by 3 equals 3 (since 3 times 3 equals 9), - and there is 1 left over. In this case, 1 is the remainder.
Edison's Phonograph Doll is a historic toy that was created by Thomas Edison in the late 19th century. It was one of the first examples of a doll that could record and play back sound, specifically using Edison's phonograph technology. The doll featured a small phonograph mechanism inside its body, allowing it to reproduce sound when a crank was turned. The doll was typically made from porcelain or composition materials and would often be dressed in elaborate clothing.
Joey Stivic is a fictional character from the American television sitcom "All in the Family," which aired from 1971 to 1979. He is the son of the show's main characters, Archie and Edith Bunker. Joey is portrayed as the grandson of the Bunkers, and the character is known for being a toddler during most of the show's run.
2020-12: buying Miele SF AP 50 AirClean Plus filter www.miele.co.uk/e/airclean-plus-filter-sf-ap-50-10107860-p. Once it arrived, changed the filter, which fit comes with plastic casing and accordion shaped filter. Also changed bag. But the bag full meter still goes to red on carpet even with everything new while vacuuming. Is it supposed to be checked while not vacuuming?
  • battery life:
    • 2023-04: on-browser streaming + light browsing on Ubuntu 22.10: about 2h45. Too low! Gotta try buying a new battery.
  • 2022-01-04 updated firmward after noticing that ubuntu 21.10 does not wake up from suspend seemed to happen every time when not connected to external power. dmidecode diff excerpt:
     BIOS Information
            Vendor: LENOVO
    -       Version: N1UET40W (1.14 )
    -       Release Date: 09/28/2017
    +       Version: N1UET71W (1.45 )
    +       Release Date: 07/18/2018
    used the "Ubuntu Software" GUI as mentioned at: support.lenovo.com/gb/en/solutions/ht510810-how-to-do-software-updates-linux. Kudos for making this accessible to newbs.
    After doing that, another update became available to: 0.1.56, clicked it and was much faster than the previous one, and didn't auto reboot. After manual reboot, dmidecode diffed again:
     BIOS Information
            Vendor: LENOVO
    -       Version: N1UET71W (1.45 )
    -       Release Date: 07/18/2018
    +       Version: N1UET82W (1.56 )
    +       Release Date: 08/12/2021
    plus a bunch of other lines.
  • 2021-06-05 upgraded to Ubuntu 21.04 with a clean install from an ISO. Selected
    • "Minimal installation"
    • "Erase disk and install Ubuntu". Notably, this erased the Microsoft Windows that came with the computer and was never used not even once
    • "Erase disk ans use ZFS"
    • Encrypt the new Ubuntu installation for security
    After this, the GUI felt fast, who would have thought that erasing a bunch of stuff would make the system faster!
    lsblk contains:
    zd0               230:0    0   500M  0 disk
    └─keystore-rpool  253:0    0   484M  0 crypt /run/keystore/rpool
    nvme0n1           259:0    0 476.9G  0 disk
    ├─nvme0n1p1       259:1    0   512M  0 part  /boot/efi
    ├─nvme0n1p2       259:2    0     2G  0 part
    │ └─cryptoswap    253:1    0     2G  0 crypt
    ├─nvme0n1p3       259:3    0     2G  0 part
    └─nvme0n1p4       259:4    0 472.4G  0 part
    and lsblk -f:
    zd0               crypto_LUKS 2
    └─keystore-rpool  ext4        1.0   keystore-rpool
    nvme0n1
    ├─nvme0n1p1       vfat        FAT32
    ├─nvme0n1p2       crypto_LUKS 2
    │ └─cryptoswap
    ├─nvme0n1p3       zfs_member  5000  bpool
    └─nvme0n1p4       zfs_member  5000  rpoo
    Then:
    grep '[rb]pool' /proc/mounts
    contains:
    rpool/ROOT/ubuntu_uvs1fq / zfs rw,relatime,xattr,posixacl 0 0
    rpool/USERDATA/ciro_czngbg /home/ciro zfs rw,relatime,xattr,posixacl 0 0
    rpool/USERDATA/root_czngbg /root zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/srv /srv zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/usr/local /usr/local zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/games /var/games zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/log /var/log zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/lib /var/lib zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/mail /var/mail zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/snap /var/snap zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/www /var/www zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/spool /var/spool zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/lib/AccountsService /var/lib/AccountsService zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/lib/NetworkManager /var/lib/NetworkManager zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/lib/apt /var/lib/apt zfs rw,relatime,xattr,posixacl 0 0
    rpool/ROOT/ubuntu_uvs1fq/var/lib/dpkg /var/lib/dpkg zfs rw,relatime,xattr,posixacl 0 0
    bpool/BOOT/ubuntu_uvs1fq /boot zfs rw,nodev,relatime,xattr,posixacl 0 0
    which gives an idea of how the above map to mountpoints.
    Had two GUI freezes since installation, a fixed images shows no matter what I do, possibly graphics only, but impossible to tell (next time I'll try SSH access). No Nvidia drivers installed yet.
2020-06-06: dropped some lemon juice on the bottom left of touchpad. Bottom left button not working anymore... I'm an idiot. There are many other alternatives, but very aggravating, I'll replace it for sure. Can't find the exact replacement part or any videos showing its replacement online easliy, dang. For the T430: www.youtube.com/watch?v=F3lzV9uXRjU Asked at: forums.lenovo.com/t5/ThinkPad-P-and-W-Series-Mobile-Workstations/P51-left-bottom-button-below-trackpad-mouse-left-click-stopped-working-possible-to-replace/m-p/5019903 Also I could not access it because you need to remove the HDD first: www.youtube.com/watch?v=5Klawxc7T_Y and I can't pull it out even with considerable force, unlike in the video... And OMG, those button caps are impossible to re-install once removed!!! Then when I put the whole thing back together, the upper buttons were not working anymore. FUUUUUUUUCK. When first opening I pulled on it without properly removing the cap and it came off, but it didn't look broken in any way and I put it back in. Keyboard works thank God, so right black connector is fine, left white one oppears to be the one for upper keys and trackpoint, both of which stopped working. The hardware manual confirms that they are both part of the same device, so basically a mouse :-) TODO can it be bought separately from te keyboard? Doesn't look like it, photo of keyboard part includes those buttons. The manual also confirms that the bottom buttons are one device with the trackpad "trackpad with buttons", thus forming the second entire mouse.
2019-04-17: popup asking about "ThinkPad P51 Management Engine Update" from from 182.29.3287 to 184.60.3561, said yes.
Ubuntu 17.10 setup after buying it:
Battery life shown by Ubuntu battery app after installation:
  • before NVIDIA driver setup: 8h
  • after: 6.5h
Equations of motion by Ciro Santilli 40 Updated 2025-07-16
These are the final equations that you derive from the Lagrangian via the Euler-Lagrange equation which specify how the system evolves with time.
  • upload all of cirosantilli.com to ourbigbook.com. I will do this by implementing an import from filesystem functionality based on the OurBigBook CLI. This will also require implementing slit headeres on the server to work well, I'll need to create one Article for every header on render.
  • get \x and \Include working on the live web preview editor. This will require creating a new simple API, currently the editor jus shows broken references, but final render works because it goes through the database backend
  • implement email verification signup. Finally! Maybe add some notifications too, e.g. on new comments or likes.
Point particle by Ciro Santilli 40 Updated 2025-07-16
This idealization does not seems to be possible at all in the context of Maxwell's equations with pointlike particles.
Playmates Toys is a toy company known for producing a wide range of action figures, playsets, and other toy products, particularly associated with popular entertainment franchises. Founded in 1966, the company gained significant recognition in the 1990s with the launch of its Teenage Mutant Ninja Turtles (TMNT) toys, which were based on the comic book and animated series of the same name.
Hatsuye Yamaguchi is likely a reference to a significant historical figure or event related to World War II, particularly concerning the use of atomic bombs. However, it's possible that the name may refer to a less-known individual, as there are limited widely recognized references to a person named Hatsuye Yamaguchi in popular historical accounts.
Actua Corporation is a technology-driven company that specializes in providing cloud-based software solutions and services to various industries. Its focus is primarily on vertical market software, addressing specific needs within sectors such as education, healthcare, and others. Actua operates through a range of subsidiaries and platforms, offering tailored solutions that enhance operational efficiency and improve customer experiences. Historically, Actua has utilized a model of acquiring and growing niche software companies to expand its offerings and market presence.
ChickClick was an online community and social networking platform launched in the late 1990s, aimed primarily at young women. It focused on providing a space for discussions, sharing interests, and connecting over topics such as fashion, beauty, health, and lifestyle. The platform featured user-generated content, forums, and articles, and was part of a broader trend toward creating niche online spaces for specific demographics.
The dot-com bubble, which peaked in the late 1990s and burst in 2000, had a significant impact on many internet-based companies. Here’s a list of some notable companies that were affected: 1. **Pets.com** - Known for its sock puppet mascot, it became infamous for its rapid rise and fall, shutting down in 2000. 2. **Webvan** - An online grocery delivery service that expanded quickly but went bankrupt in 2001.
Vignette Corporation was a software company known primarily for its web content management and digital experience management solutions. Founded in the late 1990s, the company gained recognition for its products that helped organizations manage and publish content on the internet. Vignette's software enabled businesses to create, manage, and deliver websites and online content more efficiently.
Flooz.com was an online payment platform that aimed to facilitate digital transactions, particularly through the use of virtual currencies and gift cards. Launched in the late 1990s, it gained some popularity as a way for users to send money and make purchases online. The service allowed people to buy Flooz, which could then be used to make payments at various online merchants. It was one of the early attempts to create a user-friendly digital payment system, much like how PayPal operates today.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact