Tips on handwriting maths?

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the tree
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Tips on handwriting maths?

Postby the tree » Tue Mar 03, 2009 8:06 pm UTC

For those of you that occasionally have to pick up a pencil (or, dare I say it, a pen) I'd like to know how you tackle these issues:
  • How do you make a sign for 'proportional to' ( [imath]\propto[/imath] ) not look like an alpha ( α )?
  • How do you make the letter p look different to the letter rho ( ρ )?
  • What other seemingly similar symbols have you had to make suitably separate?
  • On lined paper, do you leave a space between each line to allow for things like integrals that take up slightly more than a line?
  • How many lines should quotients take up? And where should they be centred?

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Re: Tips on handwriting maths?

Postby Beacons! » Tue Mar 03, 2009 9:21 pm UTC

Write a rho in one line, backwards to how you would do a p. Start at the bottom of the circle, go anticlockwise and then backwards on the page to do the tail. Then it looks good. That's what I always do.
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Harg
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Re: Tips on handwriting maths?

Postby Harg » Tue Mar 03, 2009 9:30 pm UTC

I could probably count the number of times I've written the 'proportional to' symbol in my lifetime on the fingers of one hand. A severely maimed hand would probably suffice.
I..actually everyone I know writes rho with a sort of swirl in the middle so that it doesn't connect to the vertical part. It's a national defect I suppose.
I don't think I've had to modify any of my handwriting yet, although I do find it distressing that my sums and epsilons are converging to some strange glyph.
And I don't write on lined paper. Only blank and checkered, but I just ignore the grid anyway, so yeah.

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Re: Tips on handwriting maths?

Postby ThomasS » Tue Mar 03, 2009 9:38 pm UTC

the tree wrote:For those of you that occasionally have to pick up a pencil (or, dare I say it, a pen) I'd like to know how you tackle these issues:
  • How do you make a sign for 'proportional to' ( [imath]\propto[/imath] ) not look like an alpha ( α )?
  • How do you make the letter p look different to the letter rho ( ρ )?
  • What other seemingly similar symbols have you had to make suitably separate?
  • On lined paper, do you leave a space between each line to allow for things like integrals that take up slightly more than a line?
  • How many lines should quotients take up? And where should they be centred?

I tend to stretch the proportional sign out, but partially that difference is by context and memmory.

When I write or print a 'p' it has a little tail - serif I guess - in the upper left corner. Not so rho. A lot of the lower case Greek letters require care to differentiate from the corresponding Latin letters. Let's see, I'm careful to curve the sides of nu if there 'v's around, and to to emphasis the left tail of mu if there are 'm's around, and for kappa I guess I am careful that height is constant, like a small capital 'K'. I write epsilon like a backwards three so that set inclusion is different. Lower case chi is also fun to differentiate, if there are 'X's around. Little eta needs more of a tail than 'n'. An oh yes, I try to avoid lined paper, otherwise I leave a blank line if I think I'm going to need an integral or quotient of size.
Last edited by ThomasS on Tue Mar 03, 2009 9:39 pm UTC, edited 1 time in total.

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Re: Tips on handwriting maths?

Postby qinwamascot » Tue Mar 03, 2009 9:38 pm UTC

I don't use proportional to signs very much, but this is how I'd look at it. Truncate each sign (the alpha and proportionality signs) to the left of the intersection. The result is 2 intersecting curves. For alpha, the curves are approximately linear to the right, and do not inflect. For the proportionality sign, the intersection point should be a point of inflection for both curves. The proportionality sign should take up approximately 1.5-1.75 character widths, while alpha should be about the size of a regular character. The proportionality sign should have spaces on either side as well.
For rho, it's best to angle it at about a 35-40 degree angle. The self intersection point should be the only point where the curve is not smooth. For p, there should be an obvious point at the top as well.
In topology, my book uses a large X for the cartesian product, but also denotes most sets by X. It's quite annoying. I now use the pi notation anyways, but I resorted to making the product sign angled at 45 degree angles, with X at about 75 degrees.
For almost any integral, I'll write it on 2 lines. If i need text on the same line, I take the upper one. Same for quotients. If I have a quotient with another fraction in the numerator or denominator, I write that one horizontally using /. I avoid writing larger fractions.
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Re: Tips on handwriting maths?

Postby Qoppa » Tue Mar 03, 2009 10:24 pm UTC

All large operators span two lines. So an integral, summation, capital pi for product, large union, etc all take up two lines. Occasionally I'll just ignore the lines when writing math.

I cross my Z's (upper case and lower case) so that they don't look like 2's. I write a cursive l when it's a variable so that it doesn't look like a 1, and sometimes I add serifs to my 1's to remove any ambiguity. I write my x's when they're variables with two strokes: a backwards 'c' and then a 'c'. An x that looks like a cross is for cross product or Cartesian product.

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Re: Tips on handwriting maths?

Postby Incompetent » Tue Mar 03, 2009 10:33 pm UTC

I have a question: do you guys write capital Pi with or without serifs at the top? I tend to write it without serifs to distinguish it from small pi, and because it doesn't have serifs in most sans-serif typefaces. (My handwriting has few serifs generally because they don't add anything to legibility unless they are drawn very neatly.) But I notice most people write it just like a tall version of the lower-case pi, perhaps to distinguish it from a 'square cap'.

Also, how are people on script letters, and 'gothic' letters? I make most of them up as I go along, but it's difficult to think of ways to distinguish them from each other and from Roman letters while making it clear which letter of the alphabet you've scrawled.

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Re: Tips on handwriting maths?

Postby Tac-Tics » Tue Mar 03, 2009 10:35 pm UTC

the tree wrote:How do you make a sign for 'proportional to' ( [imath]\propto[/imath] ) not look like an alpha ( α )?


Don't use that symbol in the first place. Just spell it out. The most prevelant use of alpha is a scalar value anyway, and if you're saying one thing is proportional to another, you can usually drop the scalar.

How do you make the letter p look different to the letter rho ( ρ )?


Emphasize the squareness of the upper part of p. Write your p's in two strokes and your rhos in one.

What other seemingly similar symbols have you had to make suitably separate?


2's and z's and t's and +'s are far more common. I write my z's with a strike through. I write my t's with an emphasis on the tail at the bottom, but when I'm writing quickly, I still have trouble sometimes.

On lined paper, do you leave a space between each line to allow for things like integrals that take up slightly more than a line?


I usually leave a space between complicated lines, in case I need to make corrections or add notes above them. If I have a fraction that is somewhat complicated, I'll throw it on two lines.

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Re: Tips on handwriting maths?

Postby the tree » Tue Mar 03, 2009 10:40 pm UTC

Incompetent wrote:I have a question: do you guys write capital Pi with or without serifs at the top? I tend to write it without serifs to distinguish it from small pi, and because it doesn't have serifs in most sans-serif typefaces. (My handwriting has few serifs generally because they don't add anything to legibility unless they are drawn very neatly.) But I notice most people write it just like a tall version of the lower-case pi, perhaps to distinguish it from a 'square cap'.
I write the lower case really curly, so much so that the 'legs' more or less come from one point. Capital pi is all straight lines.
Incompetent wrote:Also, how are people on script letters, and 'gothic' letters? I make most of them up as I go along, but it's difficult to think of ways to distinguish them from each other and from Roman letters while making it clear which letter of the alphabet you've scrawled.
For script I try to just put loops in when they normally wouldn't be there, like when there is a long straight line, I'll go over it twice to make it a loop. For gothic I tend to use black-board-bold-esque straight lines.

Qoppa wrote:I write my x's when they're variables with two strokes: a backwards 'c' and then a 'c'. An x that looks like a cross is for cross product or Cartesian product.
That reminds me of a conversation I had in highschool, with the smartest kid in the class:

Smart kid: damnit, I've written an [imath]x[/imath] wrong. What the hell is wrong with me?
Me: How did you write it wrong?
Sk: I did the curve that was supposed to be on the right, on the left, and the one that's supposed to be on the left on the right.
Me: ...
Me: ...
Me: So... instead of an [imath]x[/imath], you wrote... a circle?
Sk: Yeah.
Me: You're an idiot.
Sk: Yeah.

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Re: Tips on handwriting maths?

Postby Xanthir » Tue Mar 03, 2009 10:49 pm UTC

the tree wrote:For those of you that occasionally have to pick up a pencil (or, dare I say it, a pen) I'd like to know how you tackle these issues:
  • How do you make a sign for 'proportional to' ( [imath]\propto[/imath] ) not look like an alpha ( α )?
  • How do you make the letter p look different to the letter rho ( ρ )?
  • What other seemingly similar symbols have you had to make suitably separate?
  • On lined paper, do you leave a space between each line to allow for things like integrals that take up slightly more than a line?
  • How many lines should quotients take up? And where should they be centred?

1) I stretch it out, so it's about two characters long.

2) I draw a p by starting at the top of the vertical line, going down, then coming back up and shifting into a clockwise circle. I draw a rho by starting at the bottom of the tail (slightly serif), and in one fluid motion move up and into the clockwise circle. The two end up looking completely different.

3) I learned to draw my lowercase u without a downstroke at the end, so that it's distinct from several other letters (if I'm writing quickly, my r, v, s, n, and u look similar). I now cross my z to keep it from looking like a 2. I draw my 5 in two strokes (body first, then the top horizontal line) to keep it from looking like an s.

4) I try to. When I forget I end up hating myself.

5) Depends on how complex they are. If num/den are whole numbers, quotients use a diagonal line, like x/4. If they're simple expressions, I just write half-size. If they're complex, I write larger and let the num/den bleed into the prev/next line (which is why I try to skip lines).
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Re: Tips on handwriting maths?

Postby mister k » Wed Mar 04, 2009 10:17 am UTC

Man, I could moan for a decade about the frustrating habit in mathematics of symbols to look like each other-rho and p, u and v. Indeed, during one first year course I was half asleep while writing out a derivation of Euler's pressure law (I think... something fairly complicated with many rhos and ps...) and completely confused myself later. It meant that I had to derive the damn thing myself...

I try and avoid using similar notation, but my rho's now look rather different to my ps- I make them swirly at the bottom. I have a tendency to stylise my greek letters beyond what is necessary, or accurate, figuring consistency is more useful.
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Re: Tips on handwriting maths?

Postby auteur52 » Wed Mar 04, 2009 10:32 am UTC

I think I just finally got used to writing xi and zeta enough that they are starting to look right. I would say they're the toughest to write (except maybe aleph, still haven't really figured that one out).

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Re: Tips on handwriting maths?

Postby Torn Apart By Dingos » Wed Mar 04, 2009 11:30 am UTC

I write ~ for proportionality instead of the symbol that almost looks like an alpha.

I have difficulty telling apart [imath]\vartheta, \nu, \upsilon, v[/imath] (vartheta, nu, upsilon, v). I treat the first three as the same letter, and write them all as vartheta.

I'm pretty good at writing zeta, but small xi is still a struggle for me. I usually just replace it by epsilon if i'm not already using one.

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Re: Tips on handwriting maths?

Postby Matterwave1 » Thu Mar 05, 2009 3:59 am UTC

I hate writing kappa and k, also i hate writing lower case xi ... I can never get the swirls right. (Also looks like lower case Zeta sometimes)

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Re: Tips on handwriting maths?

Postby ++$_ » Thu Mar 05, 2009 9:40 am UTC

the tree wrote:How do you make a sign for 'proportional to' ( [imath]\propto[/imath] ) not look like an alpha ( α )?
I use a tilde (~) instead of the proportional sign.
How do you make the letter p look different to the letter rho ( ρ )?
Rho leans well over to the right, sits higher on the line, and the vertical stroke doesn't extend beyond the curved part. p stands up straight, sits low on the line, and the vertical stroke extends beyond the curved part (and is doubled, the way I write it).
What other seemingly similar symbols have you had to make suitably separate?
u, nu and v; my solution is that the sides of a v are both roughly straight or concave down, the sides of a u are concave up, and the sides of a nu are mixed (the left side is concave down).
epsilon and set membership ("\in"): epsilon is written like a backwards 3, while \in is written like a subset symbol with an extra line (but smaller).
Subset symbol and capital C: Subset is longer and the slope near the endpoints is zero.
varphi, psi: I still haven't figured this one out, really.
On lined paper, do you leave a space between each line to allow for things like integrals that take up slightly more than a line?
How many lines should quotients take up? And where should they be centred?
Learn to write your integrals and sums in textstyle (with the arguments to the right of the integral or sum); this creates a much more organized page. As for quotients, I try to squeeze them into one line when possible, but if that's not I either skip a line when I reach the end or (if I'm near the end or beginning of the line) just let them obliterate part of the succeeding line.

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Re: Tips on handwriting maths?

Postby Perpy » Thu Mar 05, 2009 10:21 am UTC

I find that the most difficult thing in equations isn't separating to similar signs, but to distinguish two different values primarily expressed by the same letter. Like when my physics teacher did a complicated equations and ended up with two h's (height and Planck's constant). He had to correct the whole problem because, basically, nobody else had seen the mistake and corrected their notes. *Rant*

And, like others have mentioned, it's terribly easy to mix Greek letters with the Latin alphabet. I always have to write a very clear "tail" on the top of my small betas.
Last edited by Perpy on Sat Mar 07, 2009 6:58 pm UTC, edited 1 time in total.

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Re: Tips on handwriting maths?

Postby Luthen » Thu Mar 05, 2009 11:44 am UTC

the tree wrote:For those of you that occasionally have to pick up a pencil (or, dare I say it, a pen) I'd like to know how you tackle these issues:
  • How do you make a sign for 'proportional to' ( [imath]\propto[/imath] ) not look like an alpha ( α )?
  • How do you make the letter p look different to the letter rho ( ρ )?
  • What other seemingly similar symbols have you had to make suitably separate?
  • On lined paper, do you leave a space between each line to allow for things like integrals that take up slightly more than a line?
  • How many lines should quotients take up? And where should they be centred?
  1. I wasn't aware they were different symbols, so I guess I do nothing
  2. I write rho backwards (circle first) but put the tail out at a 30-45 degree angle
  3. tiny epsilons and Es don't play nice. Other than that I try to avoid clashes. Still can't draw an acceptable xi though.
  4. Generally complicated intergrals end up being written across two lines. I give them about 1.5-1.8 line's worth of space so there is an acceptable gap between them
  5. Depends, generally lean towards a line for the numerator and one for the denominator when things get complicated.
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Re: Tips on handwriting maths?

Postby GBog » Sat Mar 07, 2009 2:31 pm UTC

For rho, I write something between [imath]\rho[/imath] and [imath]\varrho[/imath]. Slightly left-leaning and curving to the right at the bottom. Looks quite similar to a inverted 9, but dips below the line. I rarely confuse it with p.

[imath]\{[/imath] and [imath]\xi[/imath] might be my most similar glyphs, actually, especially if I'm sloppy.

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Re: Tips on handwriting maths?

Postby aray » Sat Mar 07, 2009 4:23 pm UTC

My tips:
Give your lowercase 't' a tail so it's obviously different from a '+'
Cross your 'z' so they don't look like a '2'

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Re: Tips on handwriting maths?

Postby Ended » Sun Mar 08, 2009 12:12 am UTC

the tree wrote:How do you make a sign for 'proportional to' ( [imath]\propto[/imath] ) not look like an alpha ( α )?
I write 'proportional to' like an infinity symbol missing the very right-hand curved edge. The tails on my alpha are shorter and the round part is circular rather than elongated.

How do you make the letter p look different to the letter rho ( ρ )?
I write 'p' so that the vertical stroke extends prominently above the top of the circular part. I write 'rho' from the bottom of the stem upwards then clockwise, in one stroke, with a little leftwards-facing tail at the beginning of the stroke.

What other seemingly similar symbols have you had to make suitably separate?
Capital U and lowercase u are a nightmare. I usually just make the capital U really really big.

On lined paper, do you leave a space between each line to allow for things like integrals that take up slightly more than a line?
How many lines should quotients take up? And where should they be centred?
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Re: Tips on handwriting maths?

Postby majikthise » Sun Mar 08, 2009 1:02 am UTC

Number of lines taken per messy integral/fraction with nested subscripts is proportional to space left until the end of the page.
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Re: Tips on handwriting maths?

Postby Why Two Kay » Sun Mar 08, 2009 1:04 am UTC

majikthise wrote:Number of lines taken per messy integral/fraction with nested subscripts is proportional to space left until the end of the page.


This. I find myself forcing myself to cram in more lines just so that I don't have 1 or 2 awkward lines in continuation on another page. Or worse I would have to create a brand new "oh no I just ran out of space" column, where you can always tell it was not planned and the organization looks terrible.
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