{"id":5665,"date":"2020-03-14T22:07:35","date_gmt":"2020-03-15T03:07:35","guid":{"rendered":"http:\/\/steve.cooleysekula.net\/blog\/?p=5665"},"modified":"2020-03-14T22:07:44","modified_gmt":"2020-03-15T03:07:44","slug":"pi-for-dessert","status":"publish","type":"post","link":"https:\/\/steve.cooleysekula.net\/blog\/2020\/03\/14\/pi-for-dessert\/","title":{"rendered":"Pi for dessert"},"content":{"rendered":"\n
\"\"
Mmmmmmm. Pi.<\/figcaption><\/figure>\n\n\n\n

<\/p>\n\n\n\n

Let’s end this day on a note of wonder. It’s Pi Day! (March 14, or 3-14). Pi is an irrational number… it cannot be written as the ratio of two integers. It’s a number that represents the ratio of the circumference of a circle to its own diameter.<\/p>\n\n\n\n

It shows up everywhere when you try to describe nature. Here are a few of my favorite places it shows up.<\/p>\n\n\n\n

Coulomb’s Law<\/h2>\n\n\n\n

Determined from experimental evidence by Augustin de Coulomb, this describes the degree of force that one electric charge exerts on another:<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ F = k \frac{q_1 q_2}{r^2} \]\"<\/p><\/p>\n\n\n\n

Coulomb’s constant, \"k\", is written in System International Units as \"k = \frac{1}{4 \pi \varepsilon_0}\".<\/p>\n\n\n\n

Biot-Savart Law<\/h2>\n\n\n\n

This is the law that describes the magnetic field generated from an electric current. In its differential form:<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ B = \frac{\mu_0}{4 \pi} \frac{i d\ell \sin\theta}{r^2} \]\"<\/p><\/p>\n\n\n\n

General Relativity<\/h2>\n\n\n\n

The Einstein Field Equations of General Relativity can be written compactly in tensor notation as<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu} \]\"<\/p><\/p>\n\n\n\n

The Heisenberg Uncertainty Principle<\/h2>\n\n\n\n

Sure you can measure the position of a subatomic particle. Sure you can measure its momentum. But you cannot make a measurement of both of them that yields unlimited precision on them at the same time. In fact, the uncertainty on them both is bounded by this relationship:<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \Delta p \Delta x \ge \frac{h}{4\pi} \]\"<\/p><\/p>\n\n\n\n

where \"h\" is Planck’s Constant, \"6.626 \times 10^{-34} \mathrm{J \cdot s}\".<\/p>\n","protected":false},"excerpt":{"rendered":"

Let’s end this day on a note of wonder. It’s Pi Day! (March 14, or 3-14). Pi is an irrational number… it cannot be written as the ratio of two integers. It’s a number that represents the ratio of the circumference of a circle to its own diameter. It shows up everywhere when you try […]<\/p>\n","protected":false},"author":2,"featured_media":5670,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":3,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[9],"tags":[],"class_list":{"0":"post-5665","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"czr-hentry"},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/steve.cooleysekula.net\/blog\/wp-content\/uploads\/2020\/03\/Pi_Glass.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/posts\/5665","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/comments?post=5665"}],"version-history":[{"count":5,"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/posts\/5665\/revisions"}],"predecessor-version":[{"id":5671,"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/posts\/5665\/revisions\/5671"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/media\/5670"}],"wp:attachment":[{"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/media?parent=5665"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/categories?post=5665"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/steve.cooleysekula.net\/blog\/wp-json\/wp\/v2\/tags?post=5665"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}