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GIF and PNG Images for Math Symbols  

This is a collection of 1179 bit-mapped, 12-point, transparent images of mathematical letters and symbols, suitable for display on a web page. The bit maps attempt to resemble standard fonts used by the LaTeX typesetting program. Each image is provided in both GIF (Graphics Interchange Format) and PNG (Portable Network Graphics) versions. For your convenience, the images are released to public domain, so there are no copyright issues to fuss with. Just use them any way you want, with or without acknowledgement.

Contents of this page Works in ALL browsers I have tried!
—Ian G. Clark, Ph.D.

Symbol Chart    All the symbols are collected on this chart. The date at the bottom of the chart indicates the version of the chart. To retrieve the GIF version of a symbol, click on the chart, then save the image with your browser. There is also a 10 x 19 blank GIF not on the chart. You can also download the whole set. (To retrieve the PNG version, use the individual links below.)

Symbol Chart rma (8x19) rmb (8x19) rmc (7x19) rmd (8x19) rme (7x19) rmf (6x19) rmg (8x19) rmh (8x19) rmi (4x19) rmj (5x19) rmk (8x19) rml (4x19) rmm (12x19) rmn (8x19) rmo (7x19) rmp (8x19) rmq (8x19) rmr (6x19) rms (6x19) rmt (6x19) rmu (8x19) rmv (8x19) rmw (12x19) rmx (8x19) rmy (8x19) rmz (6x19) rmca (10x19) rmcb (9x19) rmcc (10x19) rmcd (10x19) rmce (9x19) rmcf (9x19) rmcg (11x19) rmch (10x19) rmci (4x19) rmcj (7x19) rmck (10x19) rmcl (9x19) rmcm (12x19) rmcn (10x19) rmco (11x19) rmcp (9x19) rmcq (11x19) rmcr (10x19) rmcs (8x19) rmct (10x19) rmcu (10x19) rmcv (10x19) rmcw (15x19) rmcx (10x19) rmcy (10x19) rmcz (8x19) a (9x19) b (8x19) c (7x19) d (9x19) e (8x19) f (9x19) g (9x19) h (10x19) i (6x19) j (7x19) k (9x19) l (6x19) m (14x19) n (10x19) o (8x19) p (10x19) q (8x19) r (8x19) s (7x19) t (7x19) u (10x19) v (9x19) w (12x19) x (10x19) y (9x19) z (9x19) ca (11x19) cb (12x19) cc (12x19) cd (12x19) ce (13x19) cf (13x19) cg (12x19) ch (14x19) ci (8x19) cj (10x19) ck (14x19) cl (10x19) cm (15x19) cn (14x19) co (12x19) cp (12x19) cq (12x19) cr (12x19) cs (11x19) ct (12x19) cu (12x19) cv (12x19) cw (16x19) cx (13x19) cy (12x19) cz (11x19) bfa (10x19) bfb (11x19) bfc (9x19) bfd (11x19) bfe (9x19) bff (8x19) bfg (10x19) bfh (11x19) bfi (6x19) bfj (7x19) bfk (10x19) bfl (6x19) bfm (16x19) bfn (11x19) bfo (10x19) bfp (11x19) bfq (11x19) bfr (9x19) bfs (8x19) bft (8x19) bfu (11x19) bfv (10x19) bfw (15x19) bfx (10x19) bfy (10x19) bfz (8x19) bfca (14x19) bfcb (13x19) bfcc (12x19) bfcd (14x19) bfce (12x19) bfcf (12x19) bfcg (14x19) bfch (15x19) bfci (8x19) bfcj (10x19) bfck (15x19) bfcl (11x19) bfcm (18x19) bfcn (15x19) bfco (13x19) bfcp (12x19) bfcq (13x19) bfcr (15x19) bfcs (10x19) bfct (12x19) bfcu (15x19) bfcv (16x19) bfcw (20x19) bfcx (14x19) bfcy (14x19) bfcz (11x19) 0 (8x19) 1 (7x19) 2 (8x19) 3 (8x19) 4 (9x19) 5 (8x19) 6 (8x19) 7 (9x19) 8 (8x19) 9 (8x19) emptyset (8x19) circleds (16x19) backp (10x19) doubles (7x19) yen (11x19) copyright (16x19) dollar (9x19) pounds (11x19) ss (8x19) flat (6x19) natural (6x19) sharp (8x19) clubsuit (11x19) diamondsuit (13x19) heartsuit (13x19) spadesuit (11x19) ddag (7x19) vareighthnote (11x19) pd (17x19) nc (16x19) alpha (12x19) beta (11x19) gamma (11x19) delta (9x19) epsilon (7x19) varepsilon (8x19) zeta (9x19) eta (9x19) theta (8x19) vartheta (10x19) iota (6x19) kappa (9x19) lambda (9x19) mu (10x19) nu (9x19) xi (8x19) pi (10x19) varpi (14x19) rho (9x19) varrho (9x19) sigma (10x19) varsigma (8x19) tau (10x19) upsilon (9x19) varphi (11x19) phi (10x19) chi (12x19) psi (12x19) omega (11x19) cgamma (10x19) cdelta (13x19) ctheta (12x19) clambda (11x19) cxi (11x19) cpi (11x19) csigma (11x19) cupsilon (11x19) cphi (11x19) cpsi (11x19) comega (11x19) aleph (10x19) varaleph (12x19) beth (13x19) gimel (9x19) daleth (11x19) amalg (11x19) riota (6x19) imath (6x19) jmath (8x19) ell (9x19) wp (10x19) re (12x19) im (12x19) partial (9x19) nabla (13x19) sum (16x19) prod (12x19) coprod (12x19) digamma (11x19) varkappa (12x19) hbar (9x19) hslash (9x19) mho (11x19) finv (9x19) game (11x19) bbbk (11x19) complement (7x19) eth (9x19) backepsilon (7x19) subscrh (14x19) subscrl (12x19) cala (13x19) calb (11x19) calc (9x19) cald (13x19) cale (10x19) calf (14x19) calg (10x19) calh (13x19) cali (11x19) calj (13x19) calk (12x19) call (11x19) calm (18x19) caln (17x19) calo (13x19) calp (13x19) calq (12x19) calr (15x19) cals (11x19) calt (13x19) calu (12x19) calv (11x19) calw (17x19) calx (14x19) caly (13x19) calz (13x19) scra (16x19) scrb (15x19) scrc (14x19) scrd (14x19) scre (12x19) scrf (16x19) scrg (13x19) scrh (19x19) scri (15x19) scrj (17x19) scrk (20x19) scrl (17x19) scrm (19x19) scrn (19x19) scro (13x19) scrp (16x19) scrq (15x19) scrr (15x19) scrs (17x19) scrt (15x19) scru (16x19) scrv (14x19) scrw (17x19) scrx (17x19) scry (16x19) scrz (17x19) bba (13x19) bbb (12x19) bbc (12x19) bbd (12x19) bbe (11x19) bbf (11x19) bbg (13x19) bbh (13x19) bbi (7x19) bbj (9x19) bbk (13x19) bbl (12x19) bbm (16x19) bbn 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subk (7x19) subl (4x19) subm (10x19) subn (6x19) subo (6x19) subp (7x19) subq (6x19) subr (5x19) subs (6x19) subt (5x19) subu (6x19) subv (6x19) subw (7x19) subx (7x19) suby (6x19) subz (7x19) sub0 (6x19) sub1 (4x19) sub2 (6x19) sub3 (6x19) sub4 (6x19) sub5 (6x19) sub6 (6x19) sub7 (6x19) sub8 (6x19) sub9 (6x19) supa (7x19) supb (6x19) supc (6x19) supd (7x19) supe (6x19) supf (6x19) supg (7x19) suph (6x19) supi (3x19) supj (6x19) supk (7x19) supl (4x19) supm (10x19) supn (6x19) supo (6x19) supp (7x19) supq (6x19) supr (5x19) sups (6x19) supt (5x19) supu (6x19) supv (6x19) supw (7x19) supx (7x19) supy (6x19) supz (7x19) sup0 (6x19) sup1 (4x19) sup2 (6x19) sup3 (6x19) sup4 (6x19) sup5 (6x19) sup6 (6x19) sup7 (6x19) sup8 (6x19) sup9 (6x19) subca (8x19) subcb (8x19) subcc (9x19) subcd (9x19) subce (9x19) subcf (9x19) subcg (9x19) subch (10x19) subci (5x19) subcj (7x19) subck (10x19) subcl (8x19) subcm (10x19) subcn (10x19) subco (8x19) subcp (8x19) subcq (8x19) subcr (9x19) subcs (7x19) subct (9x19) subcu (9x19) subcv (9x19) subcw (12x19) subcx (10x19) subcy (9x19) subcz (8x19) subinfty (10x19) sublp (3x19) subrp (3x19) subplus (9x19) subminus (9x19) supca (9x19) supcb (9x19) supcc (10x19) supcd (10x19) supce (10x19) supcf (10x19) supcg (10x19) supch (11x19) supci (6x19) supcj (8x19) supck (11x19) supcl (9x19) supcm (11x19) supcn (11x19) supco (9x19) supcp (9x19) supcq (9x19) supcr (10x19) supcs (8x19) supct (10x19) supcu (10x19) supcv (10x19) supcw (13x19) supcx (11x19) supcy (10x19) supcz (9x19) supinfty (11x19) suplp (3x19) suprp (3x19) supplus (9x19) supminus (9x19) subalpha (9x19) subbeta (9x19) subgamma (9x19) subdelta (7x19) subepsilon (6x19) subvarepsilon (7x19) subzeta (7x19) subeta (8x19) subtheta (7x19) subvartheta (9x19) subiota (5x19) subkappa (8x19) sublambda (8x19) submu (8x19) subnu (7x19) subxi (7x19) subpi (9x19) subvarpi (12x19) subrho (8x19) subvarrho (8x19) subsigma (8x19) subvarsigma (7x19) subtau (8x19) subupsilon (7x19) subvarphi (10x19) subphi (8x19) subchi (9x19) subpsi (9x19) subomega (9x19) subeq (10x19) sublt (9x19) suble (9x19) subgt (9x19) subge (9x19) supalpha (9x19) supbeta (9x19) supgamma (9x19) supdelta (7x19) supepsilon (6x19) supvarepsilon (7x19) supzeta (7x19) supeta (8x19) suptheta (7x19) supvartheta (9x19) supiota (5x19) supkappa (8x19) suplambda (8x19) supmu (8x19) supnu (7x19) supxi (7x19) suppi (9x19) supvarpi (12x19) suprho (8x19) supvarrho (8x19) supsigma (8x19) supvarsigma (7x19) suptau (8x19) supupsilon (7x19) supvarphi (10x19) supphi (8x19) supchi (9x19) suppsi (9x19) supomega (9x19) supeq (10x19) suplt (9x19) suple (9x19) supgt (9x19) supge (9x19) llangle (6x19) llbrack (7x19) rrangle (6x19) rrbrack (7x19) vdvdash (16x19) lt (11x19) join (10x19) percent (13x19) minus (11x19) shortminus (8x19) period (4x19) smallprime (5x19) atsign (14x19) bigdiamond (11x19) semicolon (4x19) checkmark (11x19) bigbox (13x19) comma (4x19) plus (13x19) eq (12x19) colon (4x19) notsubset (12x19) backtick (4x19) apostrophe (4x19) backquote (7x19) quote (7x19) octothorpe (13x19) vdots (4x19) ldots (18x19) notapprox (13x19) maltese (13x19) notsucccurlyeq (11x19) questionmark (8x19) invquestion (8x19) ddots (14x19) gt (11x19) notpreccurlyeq (11x19) notsupset (12x19) cdots (16x19) largetimes (11x19) acute (5x19) bar (8x19) vec (8x19) dot (3x19) ddot (5x19) hat (7x19) supfrown (8x19) grave (5x19) tilde (8x19) check (7x19) breve (6x19) supast (6x19) subin (7x19) notsim (12x19) bigtriangleup (13x19) bigtriangledown (13x19) vee (11x19) wedge (11x19) oplus (13x19) ominus (13x19) otimes (13x19) oslash (13x19) odot (13x19) dagger (7x19) amp (12x19) le (11x19) prec (11x19) preceq (11x19) ll (16x19) subset (12x19) subseteq (12x19) sqsubseteq (12x19) in (10x19) vdash (10x19) smile (15x19) frown (16x19) ne (12x19) ge (11x19) succ (11x19) succeq (11x19) gg (16x19) supset (12x19) supseteq (12x19) sqsupseteq (11x19) owns (10x19) dashv (10x19) parallel (5x19) notin (10x19) equiv (12x19) sim (13x19) simeq (13x19) asymp 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(13x19) bigodot (17x19) bigotimes (17x19) bigoplus (17x19) bigwedge (13x19) int (10x19) oint (9x19) lp (5x19) rp (5x19) lfloor (6x19) rfloor (6x19) vert (3x19) lbrack (5x19) rbrack (5x19) lceil (6x19) rceil (7x19) lbrace (6x19) rbrace (6x19) langle (4x19) rangle (4x19) solidus (6x19) bang (3x19) downdownarrows (12x19) lplp (7x19) rprp (7x19) downarrow (7x19) invbang (3x19) vartriangle (11x19) triangledown (11x19) square (12x19) lozenge (11x19) angle (12x19) measuredangle (12x19) nexists (9x19) backprime (6x19) varnothing (11x19) blacktriangle (11x19) blacktriangledown (11x19) blacksquare (12x19) blacklozenge (11x19) bigstar (13x19) sphericalangle (11x19) diagup (14x19) diagdown (16x19) dotplus (11x19) smallsetminus (11x19) doublecap (10x19) doublecup (10x19) barwedge (9x19) veebar (9x19) doublebarwedge (9x19) boxminus (13x19) boxtimes (13x19) boxdot (13x19) boxplus (13x19) divideontimes (12x19) ltimes (10x19) rtimes (10x19) leftthreetimes (13x19) rightthreetimes (13x19) curlywedge 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(9x19) ast (7x19) star (9x19) diamond (9x19) circ (8x19) bullet (8x19) div (12x19) cap (10x19) cup (10x19) uplus (11x19) sqcap (11x19) sqcup (11x19) triangleleft (9x19) triangleright (9x19) wr (5x19) bigcirc (17x19) pfun (15x19) ffun (15x19) psurj (15x19) bij (17x19) pinj (17x19) finj (17x19) defs (11x19) ndres (11x19) nrres (11x19) smallcirc (7x19) spot (7x19) semi (6x19) inbag (10x19) uminus (11x19) limg (6x19) rimg (6x19) lblot (6x19) rblot (6x19) osmallplus (13x19) osmalltimes (13x19) filledsquarewithdots (17x19) squarewithdots (17x19) convolution (11x19) currency (13x19) cent (8x19) wlozenge (11x19) kreuz (11x19) smiley (13x19) blacksmiley (13x19) frownie (13x19) sun (13x19) brokenvert (3x19) diameter (13x19) invdiameter (13x19) phone (16x19) recorder (11x19) clock (13x19) permil (16x19) bell (7x19) ataribox (9x19) pointer (9x19) lightning (8x19) photon (44x19) gluon (50x19) eighthnote (9x19) quarternote (6x19) halfnote (6x19) fullnote (6x19) twonotes (12x19) vhf (14x19) aplbox (13x19) aplinv (13x19) aplleftarrowbox (13x19) aplrightarrowbox (13x19) apluparrowbox (13x19) apldownarrowbox (13x19) aplinput (13x19) aplminus (13x19) apllog (13x19) aplstar (11x19) aplvertdown (11x19) aplnotdown (13x19) aplnotland (13x19) aplnotlor (13x19) aplcirc (9x19) aplcircbot (15x19) notbackslash (12x19) notslash (12x19) aplcomment (9x19) desnode (14x19) astrosun (13x19) newmoon (13x19) fullmoon (13x19) leftmoon (9x19) rightmoon (9x19) mercury (9x19) venus (9x19) mars (12x19) jupiter (11x19) saturn (9x19) uranus (9x19) neptune (11x19) asteroid number 134340 formerly known as Pluto (10x19) earth (9x19) conjunction (12x19) opposition (15x19) ascnode_or_leo (14x19) vernal_or_aries (13x19) libra (18x19) taurus (12x19) scorpio (21x19) gemini (13x19) sagittarius (12x19) cancer (16x19) capricornus (13x19) aquarius (19x19) virgo (20x19) pisces (13x19) hexstar (11x19) varhexstar (11x19) davidstar (13x19) leftcircle (8x19) leftcircleb (7x19) rightcircle (8x19) rightcircleb (7x19) leftbcircle (12x19) rightbcircle (12x19) wbox (11x19) xbox (11x19) wbowtie (11x19) wdiamond (13x19) octagon (16x19) hexagon (13x19) varhexagon (12x19) pentagon (12x19) varangle (12x19) invneg (10x19) leftturn (15x19) rightturn (15x19) wvarpropto (11x19) leadsto (17x19) varint (9x19) iint (14x19) iiint (19x19) varoint (9x19) oiint (14x19) thorn (9x19) cthorn (10x19) dh (9x19) cdh (11x19) openo (8x19) inve (8x19) moon (13x19) varuranus (9x19) varneptune (11x19) varpluto (11x19) skull (15x19) biohazard (15x19) radiation (14x19) laserbeam (25x19) textdbend (15x19) stopsign (20x19) bicycle (19x19) blitza (7x19) mayazero (19x19) jackstar (17x19) sixteenstarlight (17x19) snowflakechevron (15x19) scissorright (19x19) scissorleft (19x19) handright (20x19) handleft (20x19) bighandright (22x19) bighandleft (22x19) subrma (6x19) subrmb (7x19) subrmc (5x19) subrmd (7x19) subrme (6x19) subrmf (5x19) subrmg (6x19) subrmh (7x19) subrmi (4x19) subrmj (4x19) subrmk (7x19) subrml (4x19) subrmm (10x19) subrmn (7x19) subrmo (6x19) subrmp (7x19) subrmq (7x19) subrmr (6x19) subrms (5x19) subrmt (5x19) subrmu (7x19) subrmv (6x19) subrmw (10x19) subrmx (6x19) subrmy (7x19) subrmz (6x19) subrmca (10x19) subrmcb (8x19) subrmcc (8x19) subrmcd (9x19) subrmce (8x19) subrmcf (8x19) subrmcg (9x19) subrmch (9x19) subrmci (4x19) subrmcj (6x19) subrmck (9x19) subrmcl (7x19) subrmcm (10x19) subrmcn (9x19) subrmco (8x19) subrmcp (7x19) subrmcq (8x19) subrmcr (8x19) subrmcs (6x19) subrmct (8x19) subrmcu (8x19) subrmcv (10x19) subrmcw (14x19) subrmcx (9x19) subrmcy (10x19) subrmcz (7x19) nmegill (16x19) publicdomain (99x19)


Links to Individual Symbol PNGs    Here are links to the PNG version of each symbol in the symbol chart. (For the GIF version, click on the chart above.) Each image is an n x 19 pixel transparent PNG. The file name is the name listed followed by ".png". In most cases, whenever a lowercase alphanumeric LaTeX symbol name exists, I used it; otherwise I made up my own name. There is also a 10 x 19 blank PNG not in the table. You can also download the whole set.

Over time these images may be updated, including a change of their names.

Line in chartLinks to the PNG images on that line
1 (Roman) rma rmb rmc rmd rme rmf rmg rmh rmi rmj rmk rml rmm rmn rmo rmp rmq rmr rms rmt rmu rmv rmw rmx rmy rmz
2 (Roman caps) rmca rmcb rmcc rmcd rmce rmcf rmcg rmch rmci rmcj rmck rmcl rmcm rmcn rmco rmcp rmcq rmcr rmcs rmct rmcu rmcv rmcw rmcx rmcy rmcz
3 (math italic) a b c d e f g h i j k l m n o p q r s t u v w x y z
4 (math italic caps) ca cb cc cd ce cf cg ch ci cj ck cl cm cn co cp cq cr cs ct cu cv cw cx cy cz
5 (bold) bfa bfb bfc bfd bfe bff bfg bfh bfi bfj bfk bfl bfm bfn bfo bfp bfq bfr bfs bft bfu bfv bfw bfx bfy bfz
6 (bold caps) bfca bfcb bfcc bfcd bfce bfcf bfcg bfch bfci bfcj bfck bfcl bfcm bfcn bfco bfcp bfcq bfcr bfcs bfct bfcu bfcv bfcw bfcx bfcy bfcz
7 (digits and miscellaneous) 0 1 2 3 4 5 6 7 8 9 emptyset circleds backp doubles yen copyright dollar pounds ss flat natural sharp clubsuit diamondsuit heartsuit spadesuit ddag vareighthnote pd nc
8 (Greek) alpha beta gamma delta epsilon varepsilon zeta eta theta vartheta iota kappa lambda mu nu xi pi varpi rho varrho sigma varsigma tau upsilon varphi phi chi psi omega
9 (Greek caps) cgamma cdelta ctheta clambda cxi cpi csigma cupsilon cphi cpsi comega
10 (Hebrew and letter-like symbols) aleph varaleph beth gimel daleth amalg amalg imath jmath ell wp re im partial nabla sum prod coprod digamma varkappa hbar hslash mho finv game bbbk complement eth backepsilon subscrh subscrl
11 (calligraphic) cala calb calc cald cale calf calg calh cali calj calk call calm caln calo calp calq calr cals calt calu calv calw calx caly calz
12 (script) scra scrb scrc scrd scre scrf scrg scrh scri scrj scrk scrl scrm scrn scro scrp scrq scrr scrs scrt scru scrv scrw scrx scry scrz
13 (blackboard bold) bba bbb bbc bbd bbe bbf bbg bbh bbi bbj bbk bbl bbm bbn bbo bbp bbq bbr bbs bbt bbu bbv bbw bbx bby bbz
14 (fraktur) fraka frakb frakc frakd frake frakf frakg frakh fraki frakj frakk frakl frakm frakn frako frakp frakq frakr fraks frakt fraku frakv frakw frakx fraky frakz
15 (fraktur caps) frakca frakcb frakcc frakcd frakce frakcf frakcg frakch frakci frakcj frakck frakcl frakcm frakcn frakco frakcp frakcq frakcr frakcs frakct frakcu frakcv frakcw frakcx frakcy frakcz
16 (subscripts) suba subb subc subd sube subf subg subh subi subj subk subl subm subn subo subp subq subr subs subt subu subv subw subx suby subz sub0 sub1 sub2 sub3 sub4 sub5 sub6 sub7 sub8 sub9
17 (superscripts) supa supb supc supd supe supf supg suph supi supj supk supl supm supn supo supp supq supr sups supt supu supv supw supx supy supz sup0 sup1 sup2 sup3 sup4 sup5 sup6 sup7 sup8 sup9
18 (capital subscripts) subca subcb subcc subcd subce subcf subcg subch subci subcj subck subcl subcm subcn subco subcp subcq subcr subcs subct subcu subcv subcw subcx subcy subcz subinfty sublp subrp subplus subminus
19 (capital superscripts) supca supcb supcc supcd supce supcf supcg supch supci supcj supck supcl supcm supcn supco supcp supcq supcr supcs supct supcu supcv supcw supcx supcy supcz supinfty suplp suprp supplus supminus
20 (Greek subscripts) subalpha subbeta subgamma subdelta subepsilon subvarepsilon subzeta subeta subtheta subvartheta subiota subkappa sublambda submu subnu subxi subpi subvarpi subrho subvarrho subsigma subvarsigma subtau subupsilon subvarphi subphi subchi subpsi subomega subeq sublt suble subgt subge
21 (Greek superscripts) supalpha supbeta supgamma supdelta supepsilon supvarepsilon supzeta supeta suptheta supvartheta supiota supkappa suplambda supmu supnu supxi suppi supvarpi suprho supvarrho supsigma supvarsigma suptau supupsilon supvarphi supphi supchi suppsi supomega supeq suplt suple supgt supge
22 llangle llbrack rrangle rrbrack vdvdash lt join percent minus shortminus period smallprime atsign bigdiamond semicolon checkmark bigbox comma plus eq colon notsubset backtick apostrophe backquote quote octothorpe
23 vdots ldots notapprox maltese notsucccurlyeq questionmark invquestion ddots gt notpreccurlyeq notsupset cdots largetimes acute bar vec dot ddot hat supfrown grave tilde check breve supast subin notsim
24 bigtriangleup bigtriangledown vee wedge oplus ominus otimes oslash odot dagger amp le prec preceq ll subset subseteq sqsubseteq in
25 vdash smile frown ne ge succ succeq gg supset supseteq sqsupseteq owns dashv parallel notin equiv sim simeq
26 asymp approx cong bowtie propto models doteq perp supperp infty smallint prime surd top forall exists lnot leftarrow bigleftarrow to subto bigto
27 leftrightarrow bigleftrightarrow uparrow updownarrow nearrow swarrow mapsto hookleftarrow leftharpoonup rightharpoonup rightleftharpoons longleftarrow biglongleftarrow onetoone onto
28 longrightarrow biglongrightarrow longleftrightarrow biglongleftrightarrow biguparrow bigdownarrow bigupdownarrow searrow nwarrow longmapsto hookrightarrow leftharpoondown rightharpoondown onetooneonto
29 bigvee bigcap bigcup bigsqcup biguplus bigodot bigotimes bigoplus bigwedge int oint lp rp lfloor rfloor vert lbrack rbrack lceil rceil lbrace rbrace langle rangle solidus
30 bang downdownarrows lplp rprp downarrow invbang vartriangle triangledown square lozenge angle measuredangle nexists backprime varnothing blacktriangle blacktriangledown blacksquare blacklozenge bigstar sphericalangle diagup diagdown dotplus smallsetminus
31 doublecap doublecup barwedge veebar doublebarwedge boxminus boxtimes boxdot boxplus divideontimes ltimes rtimes leftthreetimes rightthreetimes curlywedge curlyvee
32 circleddash circledast circledcirc centerdot intercal leqq leqslant eqslantless lesssim lessapprox approxeq lessdot llless lessgtr lesseqgtr lesseqqgtr
33 doteqdot risingdotseq fallingdotseq backsim backsimeq subseteqq ssubset sqsubset preccurlyeq curlyeqprec precsim precapprox vartriangleleft trianglelefteq vddash vvdash
34 smallsmile smallfrown bumpeq bbumpeq varpropto blacktriangleleft therefore geqq geqslant eqslantgtr gtrsim gtrapprox gtrdot gggtr
35 gtrless gtreqless gtreqqless eqcirc circeq triangleq thicksim thickapprox supseteqq ssupset sqsupset succcurlyeq curlyeqsucc succsim succapprox vartriangleright trianglerighteq
36 v2dash shortmid shortparallel between pitchfork blacktriangleright because nless nleq nleqslant nleqq lneqq lneq lvertneqq lnsim lnapprox
37 ngtr ngeq ngeqslant ngeqq gneq gneqq gvertneqq gnsim gnapprox nprec npreceq precneqq precnsim precnapprox nsim nshortmid nmid
38 nvdash nv2dash ntriangleleft ntrianglelefteq nsubseteq nsubseteqq subsetneq varsubsetneq subsetneqq varsubsetneqq nsucc nsucceq succneqq succnsim succnapprox ncong
39 nshortparallel nparallel nvddash nvvddash ntriangleright ntrianglerighteq nsupseteq nsupseteqq supsetneq varsupsetneqq supsetneqq varsupsetneq leftleftarrows leftrightarrows lleftarrow
40 twoheadleftarrow leftarrowtail looparrowleft leftrightharpoons curvearrowleft circlearrowleft lsh upuparrows upharpoonleft downharpoonleft multimap leftrightsquigarrow rightrightarrows rightleftarrows rrightarrow
41 twoheadrightarrow rightarrowtail looparrowright curvearrowright circlearrowright rsh restriction downharpoonright rightsquigarrow nleftarrow nbigleftarrow nleftrightarrow nrightarrow nbigrightarrow nbigleftrightarrow
42 pm mp setminus cdot times ast star diamond circ bullet div cap cup uplus sqcap sqcup triangleleft triangleright wr bigcirc
43 pfun ffun psurj bij pinj finj defs ndres nrres smallcirc spot semi inbag uminus limg rimg lblot rblot osmallplus osmalltimes filledsquarewithdots squarewithdots convolution
44 currency cent wlozenge kreuz smiley blacksmiley frownie sun brokenvert diameter invdiameter phone recorder clock permil bell ataribox pointer lightning photon gluon eighthnote quarternote halfnote fullnote twonotes
45 vhf aplbox aplinv aplleftarrowbox aplrightarrowbox apluparrowbox apldownarrowbox aplinput aplminus apllog aplstar aplvertdown aplnotdown aplnotland aplnotlor aplcirc aplcircbot notbackslash notslash aplcomment desnode astrosun newmoon fullmoon leftmoon rightmoon
46 mercury venus mars jupiter saturn uranus neptune pluto earth conjunction opposition ascnode_or_leo vernal_or_aries libra taurus scorpio gemini sagittarius cancer capricornus aquarius virgo pisces hexstar varhexstar
47 davidstar leftcircle leftcircleb rightcircle rightcircleb leftbcircle rightbcircle wbox xbox wbowtie wdiamond octagon hexagon varhexagon pentagon varangle invneg leftturn rightturn wvarpropto leadsto varint iint iiint varoint oiint thorn cthorn dh cdh openo inve
48 moon varuranus varneptune varpluto skull biohazard radiation laserbeam textdbend stopsign bicycle blitza mayazero jackstar sixteenstarlight snowflakechevron scissorright scissorleft handright handleft bighandright bighandleft
49 (Roman subscripts) subrma subrmb subrmc subrmd subrme subrmf subrmg subrmh subrmi subrmj subrmk subrml subrmm subrmn subrmo subrmp subrmq subrmr subrms subrmt subrmu subrmv subrmw subrmx subrmy subrmz
50 (Roman capital subscripts) subrmca subrmcb subrmcc subrmcd subrmce subrmcf subrmcg subrmch subrmci subrmcj subrmck subrmcl subrmcm subrmcn subrmco subrmcp subrmcq subrmcr subrmcs subrmct subrmcu subrmcv subrmcw subrmcx subrmcy subrmcz nmegill publicdomain


How to Use the Symbols    The basic way to reference a GIF (or PNG) image on a web page is with an IMG tag. For example

<IMG SRC="forall.gif" ALIGN=TOP ALT="forall" WIDTH=10 HEIGHT=19 />

renders the symbol "forall". The symbols were designed to work with ALIGN=TOP because, experimentally, this is the only setting that behaved consistently across different browsers. The ALT attribute lets blind people and others who use text-only browsers (such as w3m, links, and lynx) read your equations. The WIDTH and HEIGHT (which is always 19) are optional but make the page load faster with fewer browser rendering quirks. You can see the WIDTH and HEIGHT in the "tool tip" that appears when you pass your cursor over the symbol chart above, or you can click on the symbol and inspect its properties in your browser. If you use WIDTH and HEIGHT make sure you get them right, for otherwise the symbol will be distorted.

When you finish editing your web page, verify that its syntax is correct with W3C's on-line HTML Validator [external]. Just because it "looks right" on your particular browser version doesn't mean it will display correctly on others.

There are a couple of ways you can mix the symbol images with the rest of your page. One way is to use special symbols mixed with the normal browser text. Here is an example of a formula from mathematical logic, "For any x, there exists a y not equal to x." The HTML source code looks like this:

<IMG SRC="forall.gif" ALIGN=TOP ALT="forall" /><I>x</I><IMG
SRC="exists.gif" ALIGN=TOP ALT="exists" /><I>y</I> <I>y</I><IMG
SRC="ne.gif" ALIGN=TOP ALT="=/=" /><I>x</I>

Spaces or line breaks between the bracketed tags affect the display. The only such space in this example is between the two y's. Here is the result (on a colored background to demonstrate the transparency):

This is what it looks like on a browser with the font size set to 12: This is what it looks like on a browser with the font size set to 10: This is what it looks like on your browser right now:
forall x exists y y =/= x forall x exists y y =/= x
forallxexistsy y=/=x

Depending on your browser settings, this may look OK. But if you set the font size to something other than the usual default 12 point size (that the symbols were designed for), the characters may not align properly.

Often a better approach is to use images for the formula's letters as well. This will guarantee that all browsers will see the same thing. Also, the letters then become "math italic," which is different from regular italic. Here is the HTML source code:

<IMG SRC="forall.gif" ALIGN=TOP ALT="forall" /><IMG
SRC="x.gif" ALIGN=TOP ALT="x" /><IMG
SRC="exists.gif" ALIGN=TOP ALT="exists" /><IMG
SRC="y.gif" ALIGN=TOP ALT="y" /> <IMG
SRC="y.gif" ALIGN=TOP ALT="y" /><IMG
SRC="ne.gif" ALIGN=TOP ALT="=/=" /><IMG
SRC="x.gif" ALIGN=TOP ALT="x" />

and here is the result, independent of your browser font setting:

forallxexistsy y=/=x

It is possible to build two-dimensional formulas by using table cells to determine the placement of symbols. For example,

<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
  <TR>
    <TD VALIGN=MIDDLE><IMG
      SRC="ch.gif" ALIGN=TOP ALT="H" /><IMG
      SRC="lp.gif" ALIGN=TOP ALT="(" /><IMG
      SRC="x.gif" ALIGN=TOP ALT="x" /><IMG
      SRC="rp.gif" ALIGN=TOP ALT=")" /><IMG
      SRC="eq.gif" ALIGN=TOP ALT="=" />
    </TD>
    <TD>
      <IMG SRC="lp.gif" WIDTH=5 HEIGHT=50 ALT="(" />
    </TD>
    <TD VALIGN=MIDDLE ALIGN=CENTER>
      <IMG SRC="varint.gif" WIDTH=9 HEIGHT=33 ALT="integral" /><BR />
    </TD>
    <TD VALIGN=MIDDLE ALIGN=CENTER>
      <TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
        <TR><TD VALIGN=TOP ALIGN=CENTER HEIGHT=21>
          <IMG SRC="supinfty.gif" ALIGN=TOP ALT="infinity">
        </TD></TR>
        <TR><TD VALIGN=BOTTOM ALIGN=LEFT HEIGHT=22>
          <IMG SRC="sub0.gif" ALIGN=TOP ALT="0" />
        </TD></TR>
      </TABLE>
    </TD>
    <TD VALIGN=MIDDLE NOWRAP> <IMG
      SRC="t.gif" ALIGN=TOP ALT="t" /><IMG
      SRC="supx.gif" ALIGN=TOP ALT="^(x" /><IMG
      SRC="supminus.gif" ALIGN=TOP ALT="-" /><IMG
      SRC="sup1.gif" ALIGN=TOP ALT="1)" /><IMG
      SRC="e.gif" ALIGN=TOP ALT="e" /><IMG
      SRC="supminus.gif" ALIGN=TOP ALT="^-" /><IMG
      SRC="supt.gif" ALIGN=TOP ALT="t" /><IMG
      SRC="d.gif" ALIGN=TOP ALT="d" /><IMG
      SRC="t.gif" ALIGN=TOP ALT="t" />
    </TD>
    <TD>
      <IMG SRC="rp.gif" WIDTH=5 HEIGHT=50 ALT=")" />
    </TD>
    <TD VALIGN=TOP>
      <IMG SRC="sub2.gif" ALT="^2" />
    </TD>
  </TR>
</TABLE>

looks like this:

H(x)= ( integral
infinity
0
t^(x-1)e^-tdt ) ^2

In the code above, the parentheses and integral sign were stretched using the HEIGHT attribute, while preserving the original WIDTH.


Semi-Automated HTML Generation    Typing in the IMG tags as described above can be tedious. Here is another way that may save you time if you have a page with many equations. We will show you how you can type this into a text editor:

The square root of 2 is irrational: ` sqr 2 e/ QQ ` ,
where ` QQ ` is the set of rational numbers.

then programatically generate HTML code that displays like this:

The square root of 2 is irrational: sqr2 e/ QQ, where QQ is the set of rational numbers.

The overall idea is very simple. You define mnemonics for your math symbols, such as sqr for the square root surd. When the program encounters these mnemonics enclosed in backticks (`), it replaces the mnemonics with the HTML code you specified for them.

I will show you how to do this by exploiting the web-page generation feature built into a program called "Metamath". Note that Metamath was designed for a completely different purpose, and you must follow the instructions below carefully to coax it into accomplishing our goal. (In principle a specialized program could be written that would be simpler to use, but I'll leave that task for someone else if they are interested. The method described here is one I use myself, and I thought it would be useful to share it.)

First, download and compile the Metamath program according to the instructions on the Metamath Home Page. For Windows, you can download the pre-compiled version metamath.exe (0.5MB) instead. Then create an input file for Metamath with a text editor (Notepad or equivalent), using the following example to guide you. You may want to copy and test this example to make sure everything works. The lines you will customize are shown in red. The 5 lines shown in black should not be modified!

$( DO NOT EDIT ANY LINE WITH A "$" ON IT! $)
$c dummy $. $( LIST YOUR MNEMONICS BELOW. $) $c
QQ 2 e/ sqr
$. $( DEFINE YOUR MNEMONICS BELOW. $) $( $t
htmldef "QQ" as "<IMG SRC='bbq.gif' ALT='QQ' ALIGN=TOP />";
htmldef "2" as "<IMG SRC='2.gif' ALT='2' ALIGN=TOP />";
htmldef "e/" as " <IMG SRC='notin.gif' ALT='e/' ALIGN=TOP /> ";
htmldef "sqr" as "<IMG SRC='surd.gif' ALT='sqr' ALIGN=TOP />";
htmldef "dummy" as ""; $) $( TYPE YOUR TEXT TO BE TRANSLATED BELOW. $) $(
The square root of 2 is irrational: ` sqr 2 e/ QQ ` ,
where ` QQ ` is the set of rational numbers.

$) dummy $a dummy $.

Call this file "dummy.mm". Here is an explanation of this file. Read it carefully.

Once you build up a collection of the "htmldef" lines you need, you can use them over and over. The Metamath master database file set.mm (7MB) has inside of it many "htmldef" lines pre-defined for you that you can clip out if you like. It also references some custom GIFs with names beginning with an underscore; you probably don't care about those but if you want them they can be found in the Metamath Proof Explorer download.

Next run the Metamath program, giving it the commands "read dummy.mm", "show statement dummy /html", and "exit". (On Windows, put the files "metamath.exe" and "dummy.mm" in the same folder. Click on "metamath.exe" to run the program.) The session will look like this, with the commands you will type shown in red:

Metamath - Version 0.07x 25-Apr-05       Type HELP for help, EXIT to exit.
MM> read dummy.mm
Reading source file "dummy.mm"...
12 lines (653 characters) were read from "dummy.mm".
The source has 3 statements; 1 are $a and 0 are $p.
No errors were found. However, proofs were not checked. Type VERIFY PROOFS *
if you want to check them.
MM> show statement dummy /html
Creating HTML file "dummy.html"...
5 typesetting statements were read from "dummy.mm".
MM> exit

The Metamath program thinks it is generating a web page for the Metamath site, and there is a lot of extra stuff in its output file "dummy.html" that is irrelevant for our purposes. To extract the relevant HTML code, open "dummy.html" in your text editor, search for the string "Description: </B>", and copy the text after it and up to the string "</TD>". Paste it into your HTML file. For our example, the code section you will copy looks like this:

The square root of 2 is irrational: <IMG SRC='surd.gif' WIDTH=14 HEIGHT=19
ALT='sqr' ALIGN=TOP /><IMG SRC='2.gif' WIDTH=8 HEIGHT=19 ALT='2' ALIGN=TOP /> <IMG
SRC='notin.gif' WIDTH=10 HEIGHT=19 ALT='e/' ALIGN=TOP /> <IMG SRC='bbq.gif'
WIDTH=13 HEIGHT=19 ALT='QQ' ALIGN=TOP />,
where <IMG SRC='bbq.gif' WIDTH=13 HEIGHT=19 ALT='QQ' ALIGN=TOP /> is the set of
rational numbers.

When pasted into your HTML file, it will display like this:

The square root of 2 is irrational: sqr2 e/ QQ, where QQ is the set of rational numbers.


Suggested Extraction Guidelines    Sometimes you may want to create your own GIFs or PNGs by extracting symbols from the symbol chart (which can be saved as "symbols.gif" by right clicking on it in your browser). For example, you may not like the cell size I chose, or you may want to have a subscript directly below a superscript, or you may want to build two-dimensional formulas, or you may feel you have improved the design of a bit map.

Each individual symbol image provided here is an n x 19 pixel transparent GIF (or PNG). The width n is the width of the symbol plus (usually) a pixel of padding on each side. If we call the bottom row 1, then roman letter "I" is aligned between rows 5 and 15 inclusive. These numbers were chosen because they will properly align the symbols with a 12-point browser fonts Times New Roman and Arial.


Creating Transparent GIFs    There are many graphics programs that can clip out images and create transparent GIFs or PNGs. One of them, The GIMP (GNU Image Manipulation Program), is a free program included with most Linux distributions, including RedHat 7.2, which we describe below. It is also available for Windows. For other graphics programs, consult your user's manual. (By the way, our image map above that lets you click on symbols in the symbol chart was created using The GIMP's Imagemap plugin.)

Here is how to use The GIMP to extract a symbol from the symbol chart and create a transparent GIF from it. We show the exact process down to each individual keystroke and mouse click, so even if you have never used The GIMP before you should have no trouble with this. We assume you have saved the symbol chart into your directory as the file symbols.gif (in the Mozilla browser, right-click on it and select "Save Image...").

Note: the "webify" plug-in must be installed in The GIMP. This happens automatically with a full install of The GIMP on RedHat 7.2.

The following instructions are for the Gnome window manager. They should be similar in KDE. You can also type "gimp" at the bash command prompt in a terminal emulation window.

  1. Click on the Gnome foot icon (Main Menu) and select Programs -> Graphics -> The GIMP.
  2. From the window titled "The GIMP", click on File, click on Open, and type "symbols.gif" in the Selection box (with directory information if applicable). Click OK.
  3. A new window, "symbols.gif-0.0 (indexed)", will open. Click on the square icon between the "_" and "X" icons in the upper-right-hand corner to expand it to full screen.
  4. Find your symbol then zoom to 1000%. Use "-" and "=" keys to zoom and the scroll bars to keep your symbol visible.
  5. Point the mouse at the upper left of the symbol, just below the dotted line, and hold it down to drag the selection box to the opposite corner just above the lower dotted line, to select an n x 19 pixel rectangle (look at the Selection status at the bottom of the screen; the second number should be 19). In your selection, include a pixel of padding on either side if desired.
  6. Let go of the mouse, then right-click on the selected area; choose Edit, then click on Copy.
  7. Right-click again, select File, click on New. In the "New Image" box, the Height should automatically default to 19. Click OK.
  8. In the new "Untitled-1.0 (RGB)" window, right-click on the image, select Edit, click on Paste. Click on the image to make the pasted image stick.
  9. Right-click on the image, select Filters, and click on "Filter all Layers".
  10. In the "Animated Filter apply" window, scroll down and click on perl-fu-webify, then click on "Apply Constant".
  11. In the perl_fu_webify window, change Colors from 32 to 0, uncheck the Autocrop box, click OK.
  12. Right-click on the image in the new "Untitled-2.0 (RBG)" window. Select File and click on "Save As...". In the "Save Image" window, type xxx.gif in the Selection box, where xxx is the name of your symbol, then click OK.
  13. In the "Export File" window, click Export. In the "Save as GIF" window, click OK.
  14. Right-click on the image in the new "Untitled-2.0 (RBG) 100%" window. Select File and click on Quit. In the "Really Quit?" box click on Quit.

Done! You have now created a transparent GIF for your symbol.


Downloads    The complete collection of GIF and PNG symbols is available as a compressed archive file. Instructions: Right-click or cmd-click (Mac) on symbols.zip (0.6MB) and select "Save Link Target As..." or the equivalent command for your browser. On Windows, right-click on the saved symbols.zip file and select "Extract...". (On other computers, use a ZIP extraction program or one of these methods.) The ZIP extraction will create a directory called "symbols". Double-click on "symbols.html" therein to navigate.


Why I Created These    The Metamath site originally used the Symbol font, which is not an HTML standard and caused problems with several browsers. I wanted to update it to Unicode [external], but Microsoft's WGL4 Unicode font, which seems to be the defacto standard for Windows, puzzlingly dropped a number of rather important mathematical symbols that were already available in the earlier Symbol font (and are part of the Unicode standard), such as "for all" and "there exists." So even though the Unicode version of this site works on essentially all other browsers, it is unclear whether it will ever work with Internet Explorer unless special fonts are installed, and few users will do that just to be able to browse this site.

But this isn't just a problem with Internet Explorer. The font designers for the fonts used by non-Microsoft browsers seem to have gone off on their own inconsistent path rather than just avail themselves of the LaTeX fonts that already exist and are in the public domain. Here is a comparison of a few of the symbols used on this site, showing the LaTeX version, our bitmaps, and the Mozilla/Firefox version. To me, the Unicode characters just don't look as good as the LaTeX font or even the bitmaps on this page. The character sizes, shapes, and weights seem awkward and oddly inconsistent: the vee and wedge are too dark, the angle brackets too light, the subset-equals squished, the aleph too small, the script P missing (requiring the wreath product P as a compromise), no special italic for math letters, intersection and union not symmetrical, the dot in less-than-dot not centered, etc. The unsmoothed version looks rough, unpleasant, and amateurish, as if it was done quickly with no regard to its appearance or even legibility: the angle brackets are asymmetrical with a spurious dot on the left bracket, and the big union is missing a leg, making it literally unreadable! With non-ClearType smoothing, some characters are smoothed and others aren't in a seemingly arbitrary way.

I don't think it's just my eccentric taste. Based on the web logs, even Mozilla/Firefox users use the GIF version of the pages almost exclusively, in spite of their much slower speed and jagged bitmaps. Of course this site defaults to the GIF version, but it also makes it easy to try the Unicode version, with a link on every proof page. Almost without exception, anyone who tries the Unicode version will look at a page or two, then go back to the GIF version.

Another effort to standardize mathematics in browsers is the MathML [external] project, but currently it requires special browsers or plug-ins.

Therefore to make the site universally accessible, the only option at the present time seems to be the use of GIF (or PNG) images for the symbols. But I could not find suitable images on the web - there always seemed to be problems ranging from copyright issues to blurry fonts clipped from PDF screen displays. For example, compare our symbols to the ones in this collection [external], which has 181 symbols [external] with oddly inconsistent quality and font weights. The collection is accompanied by a restrictive license [external] that will set you back $50 [external] for commercial use. (Hopefully you'll find our public domain collection to be a better deal!)

So, I created this bi-level (1-bit monochrome) interpretation of the standard fonts that come with the LaTeX typesetting program, to fit within the limited resolution of a 12-point browser font. I made them public domain to eliminate any concern with copyright issues.

Ultimately I hope that Unicode and MathML will make these obsolete. But unfortunately it might be several years before all standard mathematical symbols are universally available by default in web browsers.


PNGs vs. GIFs    There is a current trend towards greater use of PNG images. Among other advantages, they compress large images better than GIFs. In the U.S. Department of Defense, the PNG format is mandatory for images that require lossless compression, except for animations. The W3C has another discussion of PNG versus GIF [external].

To convert from the GIF to the PNG format, I used the program gif2png [external] with the command "gif2png -Os xxx.gif".


Symbol Chart Revision History   


Copyright Terms   

All images and text displayed on this web page are placed in the public domain by the author, per the Creative Commons Public Domain Dedication [external].


  For search engines This page was last revised on 30-Nov-2013.
Your comments are welcome: Norman Megill nm at alum dot mit dot edu
W3C HTML validation [external]