How many digits? 3. Numbers? 100 is one number. Factors? 1,2,4,5,10,20,25,50,100. Prime Factored form? 2•2•5•5 Numbers from 0 or 1 to 100? Uncountably infinite amount. Sum of the integers from 0 or 1 to 100? 5050.
“Hack” is a pretty imprecise term, but let me see if I can discern what you mean by it.
I’m guessing you mean something like “log in as me,” in a way that would allow a hacker to see your private information and take actions as you, yes? (You mentioned Facebook, so something like reading private DMs and/or making posts as you would be your concern, yes?)
First off, there are some things about software security that require specialized/professional knowledge to understand, but a lot of software security is things that you can mostly work out for yourself with no “magic” involved.
You said in your original post “without using my password”, but do for sure consider that if your password is “1234” or the word “password” or something similarly easy to guess, that’s definitely one way that hacker could gain access to your accounts without comporomising your computer.
Similarly with your “secret questions” for account recovery. (That feature is usually used let you back into your account if you forget your password.) If your answers are easy to guess, that can (depending how exactly the website acts) be used to gain access to your account.
Cookies are unique identifiers that websites give you to uniquely identify you. Websites can handle requests from thousands of different users in a single second and need to be able to keep track of which requests are for the user “TootSweet” and which are for the user “adrian rodriguez” (and which are for which of the other thousands of users.) When you visit a website and your browser doesn’t give a cookie value, the website assigns you a cookie value (typically a very large number.) Thereafter, your browser will send the cookie value to the website every time your browser sends a message ot the website.
When you log in, the website saves some information on its side saying “all messages with the cookie value 12345678 are for the user ‘adrian rodriguez’.”
So, if you’re logged into a website with the “remember me” feature, that means there’s a cookie value in your browser that the website knows is you. Anyone with that cookie value can access the website as you.
Your browser does its best to make sure that that cookie value isn’t leaked to anyone. It’s supposed to be kept a secret between the website and your browser. And unless the website isn’t following good security practices, the website only assigns very large, random numbers that are very very hard for a hacker to guess.
So in practice, for a hacker to access your accounts as you via your cookies, somehow they’d have to get your cookie value. And that cookie value only exists on your computer and on the website’s computers.
If a hacker was targeting you, they might try to trick you into giving them your cookie value. They’re not terribly easy for a casual user to find, but if a hacker walked you through the process without telling you that they were trying to steal your identity and log in as you, theoretically it could be done. That would involve following some somewhat complex and opaque steps, though. Or a hacker might try to infect your computer with a virus that would go find the cookie values where your browser keeps them and send those cookie values to the hacker. There are some other potential ways they might try to steal your cookie values, but for most users, those are pretty unlikely scenarios where the hacker would probably be walking you through it step-by-step over the phone or some such.
There have been a few times when the account of someone I knew started posting spam messages or some such. I suspect in the significant majority of cases where that’s happened, it’s been because they used a very weak password or there were viruses on their computer or phone.
If that happened to you recently or you’re concerned about that potentially happening to you in the future, changing your passwords (and switching to a password manager like “LastPass” or short of that just picking a very hard-to-guess password and not reusing the same password for multiple accounts), enabling 2-factor authentication, reporting the incident to the website(s) where your account(s) were compromised (if possible), and logging out are probably your best options.
Deleting your cookies regularly can’t hurt, but it doesn’t really do anything other than log you out of all websites. (I’m oversimplifying a little, actually. But not much. It would technically be a little safer to log out of websites when you’re done using them than delete your cookies. Logging out lets the server know to stop thinking that the cookie value number is associated with your account. Deleting your cookies just makes your computer forget the cookie value. If someone already has your cookie value for a particular website, then deleting your cookies won’t do anything to revoke their access. But logging out theoretically might in some circumstances.)
Also, deleting your cookies on your phone won’t do anything about dedicated apps that you’re logged into. So, for instance, if you’re logged into the Facebook Messenger app, deleting your cookies from your browser won’t log you out of your Facebook Messenger app.
One other thing I’ll mention. You asked if providing your email address to a website could allow a hacker to access your accounts. Think to yourself: if you only knew your email address and not your password and you were logged out of an account, could you use just the email address to log in? If the answer is “no”, then chances are the same is true for “hackers.”
Sorry. I went into this post trying to explain things simply, but it’s a complex topic! I hate that there’s an extent to which you do have to be an engineer to understand some of this stuff and make good software security decisions. But there’s definitly also an extent to which you can improve your security without a degree in computer science. I hope some of this has helped at least somewhat.
i am a software developer so i know those things, and yes it’s complex, but i was afraid because i used to use firefox with cookies disabled, and i thought it was safe, but i will not give anyone my cookie value. thank you!!
Not a direct answer to the question but one thing not noted in other answers is in computing you often work at a higher precision than you need for your final answer as the errors tend to increase each time you do a mathematical operation.
In the world of reasonably powerful hardware (laptops, desktops, servers, smart phones etc.) we’d typically work with 64 bit floating point numbers which gives pi to 15 digits (I think, not at a real computer now so can’t check). because it’s simple to do so even though we don’t need the full precision.
If it’s a Bluetooth mouse, maybe there is a phone app that can find it. The could even build a locator function (like those keychain tiles) into the mouse.
Yeah absolutely they can if you’re using poor online security. The most common would be through reused passwords since websites have breaches all the time. This can easily be mitigated with the help of a password manager and 2fa (stick with totp, passkeys and hardware security keys). The second most likely method would be through phishing schemes, where a realistic looking message from a website/app is sent to you and you input your account credentials. AI is also making this much more difficult since realistic sounding voices of loved ones can be used to trick you into sending over your account credentials but that would be more of a targetted attack. You really just need to be aware of what you’re doing, not click on links unless you were expecting them, and double check identifying information from the sender to protect yourself from this. The last method is really a targetted attack and thats social engineering. This is where a scammer calls in to support pretending to be you, with personal information most likely from online breaches, in hopes of gaining your account credentials. You would just really need to rely on your 2fa and the training of support reps to protect you from this. Mostly common with phone carriers so make sure 2fa is enabled there.
You can calculate this yourself. For example, if you’re working on an object that’s 1m in diameter and you use 3.14 to compute the circumference, then you can expect errors of up to 1m * (3.142 - 3.14) = 0.002m = 2mm.
This is almost the real answer, only in reverse. Find what the appropriate error bounds of your problem is and use continuity (it probably is continuous) to find what decimal expansion you need. Or you could probably just find a solution expressible in pi and pick the decimal approximation needed. Either way, who cares about pi?
Thank you. After thinking about it overnight, I realized I asked a wrong question. Your answer still helps greatly and get me more than half way to satiate my curiosity. Tolerance grade and example objects that require different grade/minimum pi accuracy is what I was looking for.
Not a lot, and this is why to speedup thing on some architecture, when working with (unsigned)integer you multiply by 355 then divide by 113 (it’s like 3.14159292035)
you have to remember 11 33 55 and put the bar in the middle. It is mainly small MCU like ATMEGA and co. lacking FPU, and yes old stuff like Z80 ,6502, etc.
Depends on the type of account, but here are some of the common methods of how this might happen:
The attacker could be straight up guessing the password. (One possible way to mitigate this: the website can go "wow, 10 failed login attempts from that source. I'm going to ignore all attempts from there for 24 hours.")
The attacker could be using previously exposed passwords. (One possible way to mitigate this: The websites should immediately require password reset for all users when that kind of data breach happens. For users: never use same password for multiple different services, certainly never reuse a compromised password even if it's for a different service. Also: haveibeenpwned.com)
The attacker, currently using the same network, could hijack the session. (This was a really huge problem back in the day. In this day and age, websites should be using HTTPS, which limits this very much. Still possible if the site doesn't use HTTPS, and through some other vectors, e.g. malware or hijacked network hardware).
Also: Malware is a really scary big problem in that they're rarely targeting you specifically. Why do that, when they can million people at the same time and sift through that stolen data for most valuable stuff, right?
but if i type my email into haveibeenpwned.com, the owners of the website will see my email and could try to pawn it? i’m sorry, but that is a concern i have.
Email addresses are pretty much public, you give it out to people all the time. It’s no different to giving your physical address, it allows someone to link you to a location, but your house is there anyway if someone walks down the road and wants to break in.
No, that is not the point of that website. The point of HIBP is to inform you when accounts have been compromised in the past and highlight why you need to use seperate passwords for each site. You seem to be worries about attacks called Credential Stuffing and that attack is completely useless with a different password per site.
The site creator and owner Troy Hunt is a national treasure and you can check him out online to see his ethos about security.
On the NASA front, I believe I read somewhere that NASA determined that only 40 decimal places of pi are required to define a sphere the size of the observable universe to the accuracy of +/- the width of one hydrogen atom. It seems like you could file that under “close enough.”
Just using 3 is certainly too low of a precision – unless you’re writing a major work of religious literature, of course. 3.1 is likewise unlikely to result in acceptable accuracy on a terrestrial scale. I’ve always used 3.14159 which is conveniently exactly what I can remember without looking it up and it’s always been good enough for me. I don’t think I’ve ever in my life needed to scribe a circle much larger than a couple of feet across at any rate.
Thank you, I already skimmed through that article before posting. Maybe I failed to put my question into words properly.
I want examples similar to pool/fence circumference in the article. Along the line of "We're building x, and this is the worst rounding we can go, one fewer digit and it will be off by y"
In addition to what @Pons_Aelius replied, it is also used as a benchmark/flex for computers, as to who can build a beefy enough machine or good enough card to calculate more digits of pi.
The link you provided doesn’t even answer the question because it only tells you what NASA uses and then what would happen if you used no decimals at all. So your answer is not only rude, but also lazy and unhelpful.
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