FLASHCARDS: How Math Can Instantly Improve Your Photography

Gabrielle Birchak/ April 11, 2025/ Contemporary History, Modern History

It’s Flash­card Fri­day here at Math! Sci­ence! His­to­ry! And this Fri­day, I’m bring­ing you some per­spec­tive. That was a pho­tog­ra­phy joke. Today, I will talk about some sim­ple math tricks that will help you improve your pho­tog­ra­phy. Whether using your phone or cam­era, these tricks will help get you some of the best pho­tos with a new perspective!

First, let’s use the rule of thirds. Imag­ine that your pho­to is going to be divid­ed into nine equal parts with two hor­i­zon­tal lines and two ver­ti­cal lines. It’s a grid. And your phone might even pro­vide you with a grid if you choose to access it. Use this imag­ined or applic­a­ble grid to place key ele­ments along these lines or at their inter­sec­tions for bal­anced, engag­ing photos.

Next, con­sid­er lead­ing lines. This is cool. There are nat­ur­al lines that guide the viewer’s eye towards the sub­ject. Think of roads, fences, pil­lars, or rivers. When you use these, they add depth and inter­est to your pho­tos. I will post a pic­ture of me on my web­site at mathsciencehistory.com that my hus­band Joe took when I grad­u­at­ed with my sec­ond degree. It was tak­en at the Los Ange­les Pub­lic Library in front of a giant pil­lar. I will give him the cred­it for the pho­to even though it was my idea. But it’ll give you an idea about lead­ing lines and how they help take a beau­ti­ful picture.

Next up, sym­me­try and pat­terns. These are real­ly pleas­ing to the eye, so look for sym­met­ri­cal scenes or repet­i­tive pat­terns and cen­ter your shot to empha­size them. I love sym­me­try and repet­i­tive pat­terns because they real­ly yield stun­ning results.

Then there’s some­thing I talked about a cou­ple of weeks ago, the gold­en ratio. It’s like the rule of thirds but a lot more dynam­ic. It’s a ratio that is about 1.5 to 1. So, you place your sub­ject at a point that fol­lows this small ratio for a nat­u­ral­ly appeal­ing composition.

Now, let’s talk about light and expo­sure. Math is uti­lized for this, too. Doing a call­back to the rule of thirds, if you have a line of light like a sun­set, posi­tion the hori­zon along the top or the bot­tom hor­i­zon­tal line and place the sun near one of the inter­sec­tions. This real­ly har­mo­nizes the pho­to. I know that’s a weird way to say it. But it cre­ates this bal­ance, and the eyes fall in a cer­tain way to tru­ly see the appli­ca­tion of the sun to the sun­rise or sunset.

Math is at the core of pho­tog­ra­phy, espe­cial­ly when bal­anc­ing shut­ter speed, ISO, and aper­ture to get the per­fect shot. Shut­ter speed, mea­sured in frac­tions of a sec­ond (like 1/250 or 1/1000), con­trols how long light hits the sensor—longer expo­sures let in more light but can blur fast-mov­ing objects. ISO adjusts the sensor’s sen­si­tiv­i­ty to light, with low­er num­bers (ISO 100) pro­duc­ing clear­er images and high­er num­bers (ISO 3200) adding bright­ness but also grain. Aper­ture, mea­sured in f‑stops, con­trols how wide the lens opens—lower f‑numbers (f/2.8) let in more light and blur the back­ground, while high­er f‑numbers (f/11) keep more of the scene in focus.

These three set­tings form the expo­sure tri­an­gle, where adjust­ing one requires bal­anc­ing the oth­ers to achieve prop­er expo­sure. A fast shut­ter speed (like 1/1000) requires a wider aper­ture or high­er ISO, while a slow shut­ter speed (like 1/30) may need a small­er aper­ture or low­er ISO to avoid over­ex­po­sure. Under­stand­ing these math­e­mat­i­cal rela­tion­ships helps pho­tog­ra­phers con­trol light, motion, and depth to cap­ture the per­fect image.

Anoth­er way math is used in pho­tog­ra­phy is with focal length and zoom. Focal length is mea­sured in mil­lime­ters and will define how much of the scene you want. When you zoom in or out. Pho­tog­ra­phers use math to obtain the desired focal length to con­trol how much of a scene they cap­ture and how sub­jects appear in rela­tion to their sur­round­ings. A short­er focal length (like 18mm) cap­tures a wider view, mak­ing it great for land­scapes or large scenes, while a longer focal length (like 200mm) zooms in, mak­ing dis­tant sub­jects appear clos­er and more detailed, like in wildlife or sports pho­tog­ra­phy. The choice of focal length also affects per­spec­tive. Wide-angle lens­es exag­ger­ate dis­tances, mak­ing objects seem far­ther apart, while tele­pho­to lens­es com­press space, mak­ing objects appear clos­er togeth­er. This is why a pho­to of a city sky­line tak­en with a zoom lens looks like the build­ings are stacked tight­ly togeth­er, while a wide-angle shot of the same sky­line makes them seem more spaced out. By under­stand­ing how dif­fer­ent lens­es change what we see, pho­tog­ra­phers can use focal length to cre­ate the exact com­po­si­tion and feel­ing they want in an image.

Final­ly, depth of field. Depth of field is con­trolled through aper­ture set­tings. So, let’s say you want to get a pho­to with a shal­low depth of field, which would make the back­ground blur­ry and focus on the sub­ject. In that case, a low­er F stop num­ber, which is a larg­er aper­ture, would help you get that per­fect pho­to with a blur­ry back­ground and a sharp sub­ject. Now, let’s say you want the entire scene in sharp focus. You would use a high­er F stop num­ber, which means you would use a small­er aper­ture. This increas­es the depth of field and it keeps the scene in focus.

So, there’s a snap­shot for Flash­card Fri­days here at Math! Sci­ence! His­to­ry! Math helps pho­tog­ra­phers frame the per­fect shot! Whether you’re cal­cu­lat­ing focal length or just try­ing to focus on get­ting a clear pic­ture, remem­ber that math is always in the frame, whether you notice it or not.